diff --git a/qiskit_algorithms/utils/deprecation.py b/qiskit_algorithms/utils/deprecation.py
index cde81123..722e1075 100644
--- a/qiskit_algorithms/utils/deprecation.py
+++ b/qiskit_algorithms/utils/deprecation.py
@@ -14,11 +14,11 @@
 
 import functools
 import warnings
-from typing import Any, Dict, Optional, Type
+from typing import Any, Callable, Dict, Optional, Type
 
 
 def deprecate_arguments(
-    kwarg_map: Dict[str, str],
+    kwarg_map: Dict[str, Optional[str]],
     category: Type[Warning] = DeprecationWarning,
     *,
     since: Optional[str] = None,
@@ -113,3 +113,117 @@ def _rename_kwargs(
                 )
 
                 kwargs[new_arg] = kwargs.pop(old_arg)
+
+
+# We insert deprecations in-between the description and Napoleon's meta sections. The below is from
+# https://www.sphinx-doc.org/en/master/usage/extensions/napoleon.html#docstring-sections. We use
+# lowercase because Napoleon is case-insensitive.
+_NAPOLEON_META_LINES = frozenset(
+    {
+        "args:",
+        "arguments:",
+        "attention:",
+        "attributes:",
+        "caution:",
+        "danger:",
+        "error:",
+        "example:",
+        "examples:",
+        "hint:",
+        "important:",
+        "keyword args:",
+        "keyword arguments:",
+        "note:",
+        "notes:",
+        "other parameters:",
+        "parameters:",
+        "return:",
+        "returns:",
+        "raises:",
+        "references:",
+        "see also:",
+        "tip:",
+        "todo:",
+        "warning:",
+        "warnings:",
+        "warn:",
+        "warns:",
+        "yield:",
+        "yields:",
+    }
+)
+
+
+def add_deprecation_to_docstring(
+    func: Callable, msg: str, *, since: Optional[str], pending: bool
+) -> None:
+    """Dynamically insert the deprecation message into ``func``'s docstring.
+
+    Args:
+        func: The function to modify.
+        msg: The full deprecation message.
+        since: The version the deprecation started at.
+        pending: Is the deprecation still pending?
+    """
+    if "\n" in msg:
+        raise ValueError(
+            "Deprecation messages cannot contain new lines (`\\n`), but the deprecation for "
+            f'{func.__qualname__} had them. Usually this happens when using `"""` multiline '
+            f"strings; instead, use string concatenation.\n\n"
+            "This is a simplification to facilitate deprecation messages being added to the "
+            "documentation. If you have a compelling reason to need "
+            "new lines, feel free to improve this function or open a request at "
+            "https://github.com/Qiskit/qiskit-terra/issues."
+        )
+
+    if since is None:
+        version_str = "unknown"
+    else:
+        version_str = f"{since}_pending" if pending else since
+
+    indent = ""
+    meta_index = None
+    if func.__doc__:
+        original_lines = func.__doc__.splitlines()
+        content_encountered = False
+        for i, line in enumerate(original_lines):
+            stripped = line.strip()
+
+            # Determine the indent based on the first line with content. But, we don't consider the
+            # first line, which corresponds to the format """Docstring.""", as it does not properly
+            # capture the indentation of lines beneath it.
+            if not content_encountered and i != 0 and stripped:
+                num_leading_spaces = len(line) - len(line.lstrip())
+                indent = " " * num_leading_spaces
+                content_encountered = True
+
+            if stripped.lower() in _NAPOLEON_META_LINES:
+                meta_index = i
+                if not content_encountered:
+                    raise ValueError(
+                        "add_deprecation_to_docstring cannot currently handle when a Napoleon "
+                        "metadata line like 'Args' is the very first line of docstring, "
+                        f'e.g. `"""Args:`. So, it cannot process {func.__qualname__}. Instead, '
+                        f'move the metadata line to the second line, e.g.:\n\n"""\nArgs:'
+                    )
+                # We can stop checking since we only care about the first meta line, and
+                # we've validated content_encountered is True to determine the indent.
+                break
+    else:
+        original_lines = []
+
+    # We defensively include new lines in the beginning and end. This is sometimes necessary,
+    # depending on the original docstring. It is not a big deal to have extra, other than `help()`
+    # being a little longer.
+    new_lines = [
+        indent,
+        f"{indent}.. deprecated:: {version_str}",
+        f"{indent}  {msg}",
+        indent,
+    ]
+
+    if meta_index:
+        original_lines[meta_index - 1 : meta_index - 1] = new_lines
+    else:
+        original_lines.extend(new_lines)
+    func.__doc__ = "\n".join(original_lines)