diff --git a/doc/source/whatsnew/v1.6.0.rst b/doc/source/whatsnew/v1.6.0.rst
index 07d406ae7d779..fce92f2aabc8f 100644
--- a/doc/source/whatsnew/v1.6.0.rst
+++ b/doc/source/whatsnew/v1.6.0.rst
@@ -127,6 +127,7 @@ Categorical
 Datetimelike
 ^^^^^^^^^^^^
 - Bug in :func:`pandas.infer_freq`, raising ``TypeError`` when inferred on :class:`RangeIndex` (:issue:`47084`)
+- Bug where adding a :class:`DateOffset` to a :class:`DatetimeIndex` or :class:`Series` over a Daylight Savings Time boundary would produce an incorrect result (:issue:`43784`)
 -
 
 Timedelta
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 7be7381bcb4d1..6d6999d11ed81 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -1148,6 +1148,7 @@ cdef class Day(Tick):
     _td64_unit = "D"
     _period_dtype_code = PeriodDtypeCode.D
     _reso = NPY_DATETIMEUNIT.NPY_FR_D
+    _use_relativedelta = True
 
 
 cdef class Hour(Tick):
@@ -1495,6 +1496,7 @@ cdef class BusinessMixin(SingleConstructorOffset):
     """
     Mixin to business types to provide related functions.
     """
+    _use_relativedelta = True
 
     cdef readonly:
         timedelta _offset
@@ -2068,6 +2070,7 @@ cdef class WeekOfMonthMixin(SingleConstructorOffset):
     """
     Mixin for methods common to WeekOfMonth and LastWeekOfMonth.
     """
+    _use_relativedelta = True
 
     cdef readonly:
         int weekday, week
@@ -2112,6 +2115,7 @@ cdef class YearOffset(SingleConstructorOffset):
     DateOffset that just needs a month.
     """
     _attributes = tuple(["n", "normalize", "month"])
+    _use_relativedelta = True
 
     # FIXME(cython#4446): python annotation here gives compile-time errors
     # _default_month: int
@@ -2277,6 +2281,7 @@ cdef class QuarterOffset(SingleConstructorOffset):
     # FIXME(cython#4446): python annotation here gives compile-time errors
     # _default_starting_month: int
     # _from_name_starting_month: int
+    _use_relativedelta = True
 
     cdef readonly:
         int startingMonth
@@ -2448,6 +2453,8 @@ cdef class QuarterBegin(QuarterOffset):
 # Month-Based Offset Classes
 
 cdef class MonthOffset(SingleConstructorOffset):
+    _use_relativedelta = True
+
     def is_on_offset(self, dt: datetime) -> bool:
         if self.normalize and not _is_normalized(dt):
             return False
@@ -2548,6 +2555,7 @@ cdef class SemiMonthOffset(SingleConstructorOffset):
     _default_day_of_month = 15
     _min_day_of_month = 2
     _attributes = tuple(["n", "normalize", "day_of_month"])
+    _use_relativedelta = True
 
     cdef readonly:
         int day_of_month
@@ -2750,6 +2758,7 @@ cdef class Week(SingleConstructorOffset):
     _inc = timedelta(weeks=1)
     _prefix = "W"
     _attributes = tuple(["n", "normalize", "weekday"])
+    _use_relativedelta = True
 
     cdef readonly:
         object weekday  # int or None
@@ -3027,6 +3036,7 @@ cdef class LastWeekOfMonth(WeekOfMonthMixin):
 # Special Offset Classes
 
 cdef class FY5253Mixin(SingleConstructorOffset):
+    _use_relativedelta = True
     cdef readonly:
         int startingMonth
         int weekday
@@ -3496,6 +3506,7 @@ cdef class Easter(SingleConstructorOffset):
     >>> ts + pd.offsets.Easter()
     Timestamp('2022-04-17 00:00:00')
     """
+    _use_relativedelta = True
 
     cpdef __setstate__(self, state):
         self.n = state.pop("n")
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index e96e9b44112d6..5d6941ade2849 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -694,7 +694,10 @@ def _add_offset(self, offset) -> DatetimeArray:
         assert not isinstance(offset, Tick)
 
         if self.tz is not None:
-            values = self.tz_localize(None)
+            if not offset._use_relativedelta:
+                values = self.tz_convert("utc").tz_localize(None)
+            else:
+                values = self.tz_localize(None)
         else:
             values = self
 
@@ -716,7 +719,10 @@ def _add_offset(self, offset) -> DatetimeArray:
             result = DatetimeArray._simple_new(result, dtype=result.dtype)
             if self.tz is not None:
                 # FIXME: tz_localize with non-nano
-                result = result.tz_localize(self.tz)
+                if not offset._use_relativedelta:
+                    result = result.tz_localize("utc").tz_convert(self.tz)
+                else:
+                    result = result.tz_localize(self.tz)
 
         return result
 
diff --git a/pandas/tests/tseries/offsets/test_dst.py b/pandas/tests/tseries/offsets/test_dst.py
index 9c6d6a686e9a5..9e61a119994ab 100644
--- a/pandas/tests/tseries/offsets/test_dst.py
+++ b/pandas/tests/tseries/offsets/test_dst.py
@@ -30,6 +30,8 @@
     YearEnd,
 )
 
+import pandas as pd
+import pandas._testing as tm
 from pandas.tests.tseries.offsets.test_offsets import get_utc_offset_hours
 from pandas.util.version import Version
 
@@ -228,3 +230,30 @@ def test_nontick_offset_with_ambiguous_time_error(original_dt, target_dt, offset
     msg = f"Cannot infer dst time from {target_dt}, try using the 'ambiguous' argument"
     with pytest.raises(pytz.AmbiguousTimeError, match=msg):
         localized_dt + offset
+
+
+def test_series_dst_addition():
+    # GH#43784
+    startdates = pd.Series(
+        [
+            Timestamp("2020-10-25", tz="Europe/Berlin"),
+            Timestamp("2017-03-12", tz="US/Pacific"),
+        ]
+    )
+    offset1 = DateOffset(hours=3)
+    offset2 = DateOffset(days=1)
+
+    expected1 = pd.Series(
+        [Timestamp("2020-10-25 02:00:00+01:00"), Timestamp("2017-03-12 04:00:00-07:00")]
+    )
+
+    expected2 = pd.Series(
+        [Timestamp("2020-10-26 00:00:00+01:00"), Timestamp("2017-03-13 00:00:00-07:00")]
+    )
+
+    result1 = startdates + offset1
+    result2 = startdates + offset2
+
+    tm.assert_series_equal(result1, expected1)
+
+    tm.assert_series_equal(result2, expected2)