diff --git a/package/CHANGELOG b/package/CHANGELOG
index fa139c024a5..bf9e895a954 100644
--- a/package/CHANGELOG
+++ b/package/CHANGELOG
@@ -108,6 +108,7 @@ Fixes
   * Fix tests for analysis.bat that could fail when run in parallel and that
     would create a test artifact (Issue #2979, PR #2981)
   * Fix syntax warning over comparison of literals using is (Issue #3066)
+  * new `Results` class now can be pickled/unpickled. (PR #3309) 
 
 Enhancements
   * Added guessers for aromaticity and Gasteiger partial charges (Issue #2468,
diff --git a/package/MDAnalysis/analysis/base.py b/package/MDAnalysis/analysis/base.py
index f38a24890eb..c7bb9a40293 100644
--- a/package/MDAnalysis/analysis/base.py
+++ b/package/MDAnalysis/analysis/base.py
@@ -62,10 +62,6 @@ class in `scikit-learn`_.
         If a key is not of type ``str`` and therefore is not able to be
         accessed by attribute.
 
-    Notes
-    -----
-    Pickling of ``Results`` is currently not supported.
-
     Examples
     --------
     >>> from MDAnalysis.analysis.base import Results
@@ -103,7 +99,11 @@ def __setitem__(self, key, item):
         self._validate_key(key)
         super().__setitem__(key, item)
 
-    __setattr__ = __setitem__
+    def __setattr__(self, attr, val):
+        if attr == 'data':
+            super().__setattr__(attr, val)
+        else:
+            self.__setitem__(attr, val)
 
     def __getattr__(self, attr):
         try:
@@ -119,6 +119,12 @@ def __delattr__(self, attr):
             raise AttributeError("'Results' object has no "
                                  f"attribute '{attr}'") from err
 
+    def __getstate__(self):
+        return self.data
+
+    def __setstate__(self, state):
+        self.data = state
+
 
 class AnalysisBase(object):
     r"""Base class for defining multi-frame analysis
diff --git a/testsuite/MDAnalysisTests/analysis/test_base.py b/testsuite/MDAnalysisTests/analysis/test_base.py
index 9c4995e4c07..8201a93e084 100644
--- a/testsuite/MDAnalysisTests/analysis/test_base.py
+++ b/testsuite/MDAnalysisTests/analysis/test_base.py
@@ -21,6 +21,7 @@
 # J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
 #
 from collections import UserDict
+import pickle
 
 import pytest
 
@@ -125,6 +126,10 @@ def test_update_data_fail(self, results):
         with pytest.raises(AttributeError, match=msg):
             results.update({"data": 0})
 
+    def test_pickle(self, results):
+        results_p = pickle.dumps(results)
+        results_new = pickle.loads(results_p)
+
     @pytest.mark.parametrize("args, kwargs, length", [
         (({"darth": "tater"},), {}, 1),
         ([], {"darth": "tater"}, 1),
diff --git a/testsuite/MDAnalysisTests/parallelism/test_multiprocessing.py b/testsuite/MDAnalysisTests/parallelism/test_multiprocessing.py
index 0832e907756..12e63ba31b5 100644
--- a/testsuite/MDAnalysisTests/parallelism/test_multiprocessing.py
+++ b/testsuite/MDAnalysisTests/parallelism/test_multiprocessing.py
@@ -29,6 +29,7 @@
 
 import MDAnalysis as mda
 from MDAnalysis.coordinates.core import get_reader_for
+from MDAnalysis.analysis.rms import RMSD
 
 from MDAnalysisTests.datafiles import (
     CRD,
@@ -177,3 +178,11 @@ def test_readers_pickle(ref_reader):
         # single frame files
         pass
     assert_equal(reanimated.ts, ref_reader.ts)
+
+
+def test_analysis_pickle():
+    u = mda.Universe(PSF, DCD)
+    rmsd = RMSD(u.atoms, u.atoms)
+    rmsd.run()
+    rmsd_p = pickle.dumps(rmsd)
+    rmsd_new = pickle.loads(rmsd_p)