diff --git a/docs/conf.py b/docs/conf.py
index e8cb6ec4b107..3478f6dccef2 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -34,7 +34,6 @@
     "sphinx.ext.viewcode",
     "sphinx.ext.extlinks",
     "sphinx.ext.intersphinx",
-    "sphinx_autodoc_typehints",
     "reno.sphinxext",
     "sphinx_design",
     "matplotlib.sphinxext.plot_directive",
@@ -83,6 +82,13 @@
 # documentation created by autosummary uses a template file (in autosummary in the templates path),
 # which likely overrides the autodoc defaults.
 
+# Move type hints from signatures to the parameter descriptions (except in overload cases, where
+# that's not possible).
+autodoc_typehints = "description"
+# Only add type hints from signature to description body if the parameter has documentation.  The
+# return type is always added to the description (if in the signature).
+autodoc_typehints_description_target = "documented_params"
+
 autosummary_generate = True
 autosummary_generate_overwrite = False
 
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 1df9eccacc92..dd814caf7641 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -16,9 +16,8 @@ pylatexenc>=1.4
 ddt>=1.2.0,!=1.4.0,!=1.4.3
 seaborn>=0.9.0
 reno>=3.4.0
-Sphinx>=3.0.0
+Sphinx>=5.0
 qiskit-sphinx-theme>=1.6
-sphinx-autodoc-typehints==1.21.1  # revert to >=1.18 once the incompatibilities are fixed
 sphinx-design>=0.2.0
 pygments>=2.4
 scikit-learn>=0.20.0