diff --git a/asv_bench/benchmarks/timeseries.py b/asv_bench/benchmarks/timeseries.py
index 6c9f8ee77e5ad..b494dbd8a38fa 100644
--- a/asv_bench/benchmarks/timeseries.py
+++ b/asv_bench/benchmarks/timeseries.py
@@ -336,15 +336,33 @@ def time_infer_quarter(self):
 
 class ToDatetimeFormat:
     def setup(self):
-        self.s = Series(["19MAY11", "19MAY11:00:00:00"] * 100000)
+        N = 100000
+        self.s = Series(["19MAY11", "19MAY11:00:00:00"] * N)
         self.s2 = self.s.str.replace(":\\S+$", "")
 
+        self.same_offset = ["10/11/2018 00:00:00.045-07:00"] * N
+        self.diff_offset = [
+            f"10/11/2018 00:00:00.045-0{offset}:00" for offset in range(10)
+        ] * int(N / 10)
+
     def time_exact(self):
         to_datetime(self.s2, format="%d%b%y")
 
     def time_no_exact(self):
         to_datetime(self.s, format="%d%b%y", exact=False)
 
+    def time_same_offset(self):
+        to_datetime(self.same_offset, format="%m/%d/%Y %H:%M:%S.%f%z")
+
+    def time_different_offset(self):
+        to_datetime(self.diff_offset, format="%m/%d/%Y %H:%M:%S.%f%z")
+
+    def time_same_offset_to_utc(self):
+        to_datetime(self.same_offset, format="%m/%d/%Y %H:%M:%S.%f%z", utc=True)
+
+    def time_different_offset_to_utc(self):
+        to_datetime(self.diff_offset, format="%m/%d/%Y %H:%M:%S.%f%z", utc=True)
+
 
 class ToDatetimeCache:
 
diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 692df075f25cb..83df71520ba2f 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -58,6 +58,22 @@ For example:
 
 For more on working with fold, see :ref:`Fold subsection <timeseries.fold>` in the user guide.
 
+.. _whatsnew_110.to_datetime_multiple_tzname_tzoffset_support:
+
+Parsing timezone-aware format with different timezones in to_datetime
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+:func:`to_datetime` now supports parsing formats containing timezone names (``%Z``) and UTC offsets (``%z``) from different timezones then converting them to UTC by setting ``utc=True``. This would return a :class:`DatetimeIndex` with timezone at UTC as opposed to an :class:`Index` with ``object`` dtype if ``utc=True`` is not set (:issue:`32792`).
+
+For example:
+
+.. ipython:: python
+
+    tz_strs = ["2010-01-01 12:00:00 +0100", "2010-01-01 12:00:00 -0100",
+               "2010-01-01 12:00:00 +0300", "2010-01-01 12:00:00 +0400"]
+    pd.to_datetime(tz_strs, format='%Y-%m-%d %H:%M:%S %z', utc=True)
+    pd.to_datetime(tz_strs, format='%Y-%m-%d %H:%M:%S %z')
+
 .. _whatsnew_110.enhancements.other:
 
 Other enhancements
diff --git a/pandas/core/tools/datetimes.py b/pandas/core/tools/datetimes.py
index 7414165ab5711..b922e1b318622 100644
--- a/pandas/core/tools/datetimes.py
+++ b/pandas/core/tools/datetimes.py
@@ -229,13 +229,12 @@ def _return_parsed_timezone_results(result, timezones, tz, name):
     -------
     tz_result : Index-like of parsed dates with timezone
     """
-    if tz is not None:
-        raise ValueError(
-            "Cannot pass a tz argument when parsing strings with timezone information."
-        )
     tz_results = np.array(
         [Timestamp(res).tz_localize(zone) for res, zone in zip(result, timezones)]
     )
+    if tz is not None:
+        # Convert to the same tz
+        tz_results = np.array([tz_result.tz_convert(tz) for tz_result in tz_results])
     from pandas import Index
 
     return Index(tz_results, name=name)
diff --git a/pandas/tests/tools/test_to_datetime.py b/pandas/tests/tools/test_to_datetime.py
index 6689021392a92..a751182dbf7af 100644
--- a/pandas/tests/tools/test_to_datetime.py
+++ b/pandas/tests/tools/test_to_datetime.py
@@ -323,8 +323,25 @@ def test_to_datetime_parse_tzname_or_tzoffset(self, fmt, dates, expected_dates):
         expected = pd.Index(expected_dates)
         tm.assert_equal(result, expected)
 
-        with pytest.raises(ValueError):
-            pd.to_datetime(dates, format=fmt, utc=True)
+    def test_to_datetime_parse_tzname_or_tzoffset_different_tz_to_utc(self):
+        # GH 32792
+        dates = [
+            "2010-01-01 12:00:00 +0100",
+            "2010-01-01 12:00:00 -0100",
+            "2010-01-01 12:00:00 +0300",
+            "2010-01-01 12:00:00 +0400",
+        ]
+        expected_dates = [
+            "2010-01-01 11:00:00+00:00",
+            "2010-01-01 13:00:00+00:00",
+            "2010-01-01 09:00:00+00:00",
+            "2010-01-01 08:00:00+00:00",
+        ]
+        fmt = "%Y-%m-%d %H:%M:%S %z"
+
+        result = pd.to_datetime(dates, format=fmt, utc=True)
+        expected = pd.DatetimeIndex(expected_dates)
+        tm.assert_index_equal(result, expected)
 
     @pytest.mark.parametrize(
         "offset", ["+0", "-1foo", "UTCbar", ":10", "+01:000:01", ""]