diff --git a/changelogs/upcoming/7371.md b/changelogs/upcoming/7371.md
new file mode 100644
index 00000000000..96724c7ec76
--- /dev/null
+++ b/changelogs/upcoming/7371.md
@@ -0,0 +1,6 @@
+- Updated `EuiDataGrid` column header cells to show the sort arrow after the heading text, instead of before
+- Updated `EuiDataGrid`'s column header actions icon from a chevron to `boxesVertical`
+
+**Bug fixes**
+
+- Fixed `EuiDataGrid`'s numeric and currency column heading cells to be correctly right-aligned
diff --git a/src/components/datagrid/__snapshots__/data_grid.test.tsx.snap b/src/components/datagrid/__snapshots__/data_grid.test.tsx.snap
index cf9665dca56..e35c3781496 100644
--- a/src/components/datagrid/__snapshots__/data_grid.test.tsx.snap
+++ b/src/components/datagrid/__snapshots__/data_grid.test.tsx.snap
@@ -617,12 +617,15 @@ exports[`EuiDataGrid rendering renders additional toolbar controls 1`] = `
                     >
                       A
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-A"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-A"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
@@ -667,12 +670,15 @@ exports[`EuiDataGrid rendering renders additional toolbar controls 1`] = `
                     >
                       B
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-B"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-B"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
@@ -1049,12 +1055,15 @@ exports[`EuiDataGrid rendering renders control columns 1`] = `
                     >
                       A
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-A"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-A"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
@@ -1099,12 +1108,15 @@ exports[`EuiDataGrid rendering renders control columns 1`] = `
                     >
                       B
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-B"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-B"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
@@ -1718,12 +1730,15 @@ exports[`EuiDataGrid rendering renders custom column headers 1`] = `
                     >
                       Column A
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-A"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-A"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
@@ -1770,12 +1785,15 @@ exports[`EuiDataGrid rendering renders custom column headers 1`] = `
                         More Elements
                       </div>
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-B"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-B"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
@@ -2130,12 +2148,15 @@ exports[`EuiDataGrid rendering renders with common and div attributes 1`] = `
                     >
                       A
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-A"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-A"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
@@ -2180,12 +2201,15 @@ exports[`EuiDataGrid rendering renders with common and div attributes 1`] = `
                     >
                       B
                     </div>
-                    <span
+                    <div
                       class="euiDataGridHeaderCell__icon"
-                      color="text"
-                      data-euiicon-type="arrowDown"
-                      data-test-subj="dataGridHeaderCellActionButton-B"
-                    />
+                    >
+                      <span
+                        color="text"
+                        data-euiicon-type="boxesVertical"
+                        data-test-subj="dataGridHeaderCellActionButton-B"
+                      />
+                    </div>
                   </button>
                 </div>
                 <p
diff --git a/src/components/datagrid/body/__snapshots__/data_grid_body_custom.test.tsx.snap b/src/components/datagrid/body/__snapshots__/data_grid_body_custom.test.tsx.snap
index d17d29bfa94..ce1b952cb4d 100644
--- a/src/components/datagrid/body/__snapshots__/data_grid_body_custom.test.tsx.snap
+++ b/src/components/datagrid/body/__snapshots__/data_grid_body_custom.test.tsx.snap
@@ -40,12 +40,15 @@ exports[`EuiDataGridBodyCustomRender treats \`renderCustomGridBody\` as a render
           >
             columnA
           </div>
-          <span
+          <div
             class="euiDataGridHeaderCell__icon"
-            color="text"
-            data-euiicon-type="arrowDown"
-            data-test-subj="dataGridHeaderCellActionButton-columnA"
-          />
+          >
+            <span
+              color="text"
+              data-euiicon-type="boxesVertical"
+              data-test-subj="dataGridHeaderCellActionButton-columnA"
+            />
+          </div>
         </button>
       </div>
       <p
@@ -90,12 +93,15 @@ exports[`EuiDataGridBodyCustomRender treats \`renderCustomGridBody\` as a render
           >
             columnB
           </div>
-          <span
+          <div
             class="euiDataGridHeaderCell__icon"
-            color="text"
-            data-euiicon-type="arrowDown"
-            data-test-subj="dataGridHeaderCellActionButton-columnB"
-          />
+          >
+            <span
+              color="text"
+              data-euiicon-type="boxesVertical"
+              data-test-subj="dataGridHeaderCellActionButton-columnB"
+            />
+          </div>
         </button>
       </div>
       <p
diff --git a/src/components/datagrid/body/__snapshots__/data_grid_body_virtualized.test.tsx.snap b/src/components/datagrid/body/__snapshots__/data_grid_body_virtualized.test.tsx.snap
index 7452e75b2c3..136a1d28110 100644
--- a/src/components/datagrid/body/__snapshots__/data_grid_body_virtualized.test.tsx.snap
+++ b/src/components/datagrid/body/__snapshots__/data_grid_body_virtualized.test.tsx.snap
@@ -44,12 +44,15 @@ exports[`EuiDataGridBodyVirtualized renders 1`] = `
             >
               columnA
             </div>
-            <span
+            <div
               class="euiDataGridHeaderCell__icon"
-              color="text"
-              data-euiicon-type="arrowDown"
-              data-test-subj="dataGridHeaderCellActionButton-columnA"
-            />
+            >
+              <span
+                color="text"
+                data-euiicon-type="boxesVertical"
+                data-test-subj="dataGridHeaderCellActionButton-columnA"
+              />
+            </div>
           </button>
         </div>
         <p
@@ -94,12 +97,15 @@ exports[`EuiDataGridBodyVirtualized renders 1`] = `
             >
               columnB
             </div>
-            <span
+            <div
               class="euiDataGridHeaderCell__icon"
-              color="text"
-              data-euiicon-type="arrowDown"
-              data-test-subj="dataGridHeaderCellActionButton-columnB"
-            />
+            >
+              <span
+                color="text"
+                data-euiicon-type="boxesVertical"
+                data-test-subj="dataGridHeaderCellActionButton-columnB"
+              />
+            </div>
           </button>
         </div>
         <p
diff --git a/src/components/datagrid/body/header/__snapshots__/data_grid_header_cell.test.tsx.snap b/src/components/datagrid/body/header/__snapshots__/data_grid_header_cell.test.tsx.snap
index 06ab274175e..10392536413 100644
--- a/src/components/datagrid/body/header/__snapshots__/data_grid_header_cell.test.tsx.snap
+++ b/src/components/datagrid/body/header/__snapshots__/data_grid_header_cell.test.tsx.snap
@@ -32,12 +32,15 @@ exports[`EuiDataGridHeaderCell renders 1`] = `
       >
         someColumn
       </div>
-      <span
+      <div
         class="euiDataGridHeaderCell__icon"
-        color="text"
-        data-euiicon-type="arrowDown"
-        data-test-subj="dataGridHeaderCellActionButton-someColumn"
-      />
+      >
+        <span
+          color="text"
+          data-euiicon-type="boxesVertical"
+          data-test-subj="dataGridHeaderCellActionButton-someColumn"
+        />
+      </div>
     </button>
   </div>
   <p
diff --git a/src/components/datagrid/body/header/_data_grid_header_row.scss b/src/components/datagrid/body/header/_data_grid_header_row.scss
index c17b5293aed..283a1822227 100644
--- a/src/components/datagrid/body/header/_data_grid_header_row.scss
+++ b/src/components/datagrid/body/header/_data_grid_header_row.scss
@@ -17,14 +17,6 @@
   align-items: center;
   display: flex;
 
-  &.euiDataGridHeaderCell--numeric {
-    text-align: right;
-  }
-
-  &.euiDataGridHeaderCell--currency {
-    text-align: right;
-  }
-
   &:focus {
     @include euiDataGridCellFocus;
     border-top: none;
@@ -37,38 +29,58 @@
       border-top: none;
     }
 
-    .euiDataGridHeaderCell__sortingArrow {
-      margin-right: $euiSizeXS;
-    }
-
     .euiDataGridHeaderCell__button {
-      flex: 0 0 auto;
       position: relative;
-      align-items: center;
       display: flex;
+      align-items: center;
+      gap: $euiSizeXS;
       width: 100%;
       font-weight: $euiFontWeightBold;
       outline: none;
-
-      .euiDataGridHeaderCell__sortingArrow {
-        flex-grow: 0;
-      }
     }
 
     .euiDataGridHeaderCell__content {
       @include euiTextTruncate;
+    }
+
+    .euiDataGridHeaderCell__sortingArrow {
+      flex: 0 0 auto; // Ensure icon doesn't shrink
+    }
+
+    .euiDataGridHeaderCell__icon {
+      flex: 0 0 auto; // Ensure icon doesn't shrink
+      margin-left: auto; // Aligns the icon to the right
+      // Center the icon vertically
+      display: flex;
+      align-items: center;
+      height: $euiSize;
       overflow: hidden;
-      white-space: nowrap;
-      text-align: left;
-      flex-grow: 1;
-      align-self: baseline;
+      width: 0;
+      opacity: 0;
+      transition: width $euiAnimSpeedFast ease-in, opacity $euiAnimSpeedSlow ease-in;
+    }
+
+    &:focus-within,
+    &:hover,
+    .euiPopover-isOpen {
+      .euiDataGridHeaderCell__icon {
+        width: $euiSize;
+        opacity: 1;
+      }
+    }
+  }
+
+  // Align numeric and currency schemas to the right
+  &.euiDataGridHeaderCell--numeric,
+  &.euiDataGridHeaderCell--currency {
+    justify-content: flex-end; // Accounts for columns with disabled actions (no popover)
+
+    .euiDataGridHeaderCell__button {
+      justify-content: flex-end; // Accounts for cells with a popover
     }
 
     .euiDataGridHeaderCell__icon {
-      flex-grow: 0;
-      flex-basis: auto;
-      width: auto;
-      padding-left: $euiSizeXS;
+      margin-left: 0;
     }
   }
 }
diff --git a/src/components/datagrid/body/header/data_grid_header_cell.tsx b/src/components/datagrid/body/header/data_grid_header_cell.tsx
index 2626bc45e36..3b1921ce0ed 100644
--- a/src/components/datagrid/body/header/data_grid_header_cell.tsx
+++ b/src/components/datagrid/body/header/data_grid_header_cell.tsx
@@ -95,6 +95,18 @@ export const EuiDataGridHeaderCell: FunctionComponent<
     suffix: 'actions',
   });
 
+  const cellContent = (
+    <>
+      <div
+        title={displayAsText || id}
+        className="euiDataGridHeaderCell__content"
+      >
+        {display || displayAsText || id}
+      </div>
+      {sortingArrow}
+    </>
+  );
+
   return (
     <EuiDataGridHeaderCellWrapper
       {...displayHeaderCellProps}
@@ -115,13 +127,7 @@ export const EuiDataGridHeaderCell: FunctionComponent<
 
       {!showColumnActions ? (
         <>
-          {sortingArrow}
-          <div
-            className="euiDataGridHeaderCell__content"
-            title={displayAsText || id}
-          >
-            {display || displayAsText || id}
-          </div>
+          {cellContent}
           {sortingScreenReaderText && (
             <EuiScreenReaderOnly>
               <p>{sortingScreenReaderText}</p>
@@ -144,20 +150,15 @@ export const EuiDataGridHeaderCell: FunctionComponent<
                 }}
                 aria-describedby={`${sortingAriaId} ${actionsAriaId}`}
               >
-                {sortingArrow}
-                <div
-                  className="euiDataGridHeaderCell__content"
-                  title={displayAsText || id}
-                >
-                  {display || displayAsText || id}
+                {cellContent}
+                <div className="euiDataGridHeaderCell__icon">
+                  <EuiIcon
+                    type="boxesVertical"
+                    size="s"
+                    color="text"
+                    data-test-subj={`dataGridHeaderCellActionButton-${id}`}
+                  />
                 </div>
-                <EuiIcon
-                  className="euiDataGridHeaderCell__icon"
-                  type="arrowDown"
-                  size="s"
-                  color="text"
-                  data-test-subj={`dataGridHeaderCellActionButton-${id}`}
-                />
               </button>
             }
             isOpen={isPopoverOpen}