diff --git a/doc/api/next_api_changes/deprecations/19336-AL.rst b/doc/api/next_api_changes/deprecations/19336-AL.rst
new file mode 100644
index 000000000000..b77bca4c8cf5
--- /dev/null
+++ b/doc/api/next_api_changes/deprecations/19336-AL.rst
@@ -0,0 +1,3 @@
+Setting a Line2D's pickradius via ``set_picker`` is undeprecated
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+This cancels the deprecation introduced in Matplotlib 3.3.0.
diff --git a/lib/matplotlib/artist.py b/lib/matplotlib/artist.py
index a3dfebcaf233..ced1e002d385 100644
--- a/lib/matplotlib/artist.py
+++ b/lib/matplotlib/artist.py
@@ -539,7 +539,7 @@ def set_picker(self, picker):
 
         Parameters
         ----------
-        picker : None or bool or callable
+        picker : None or bool or float or callable
             This can be one of the following:
 
             - *None*: Picking is disabled for this artist (default).
@@ -548,6 +548,14 @@ def set_picker(self, picker):
               artist will fire a pick event if the mouse event is over
               the artist.
 
+            - A float: If picker is a number it is interpreted as an
+              epsilon tolerance in points and the artist will fire
+              off an event if its data is within epsilon of the mouse
+              event.  For some artists like lines and patch collections,
+              the artist may provide additional data to the pick event
+              that is generated, e.g., the indices of the data within
+              epsilon of the pick event
+
             - A function: If picker is callable, it is a user supplied
               function which determines whether the artist is hit by the
               mouse event::
@@ -557,11 +565,6 @@ def set_picker(self, picker):
               to determine the hit test.  if the mouse event is over the
               artist, return *hit=True* and props is a dictionary of
               properties you want added to the PickEvent attributes.
-
-            - *deprecated*: For `.Line2D` only, *picker* can also be a float
-              that sets the tolerance for checking whether an event occurred
-              "on" the line; this is deprecated.  Use `.Line2D.set_pickradius`
-              instead.
         """
         self._picker = picker
 
diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
index e502ff119253..bac48f3522c2 100644
--- a/lib/matplotlib/lines.py
+++ b/lib/matplotlib/lines.py
@@ -397,6 +397,8 @@ def __init__(self, xdata, ydata,
         self.update(kwargs)
         self.pickradius = pickradius
         self.ind_offset = 0
+        if isinstance(self._picker, Number):
+            self.pickradius = self._picker
 
         self._xorig = np.asarray([])
         self._yorig = np.asarray([])
@@ -601,13 +603,17 @@ def get_markevery(self):
         return self._markevery
 
     def set_picker(self, p):
-        # docstring inherited
-        if isinstance(p, Number) and not isinstance(p, bool):
-            # After deprecation, the whole method can be deleted and inherited.
-            _api.warn_deprecated(
-                "3.3", message="Setting the line's pick radius via set_picker "
-                "is deprecated since %(since)s and will be removed "
-                "%(removal)s; use set_pickradius instead.")
+        """
+        Sets the event picker details for the line.
+
+        Parameters
+        ----------
+        p : float or callable[[Artist, Event], Tuple[bool, dict]]
+            If a float, it is used as the pick radius in points.
+        """
+        if callable(p):
+            self._contains = p
+        else:
             self.pickradius = p
         self._picker = p