diff --git a/AUTHORS b/AUTHORS
index 16272bdf28..5c50598ddc 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -449,6 +449,7 @@ answer newbie questions, and generally made Django that much better:
     Joao Oliveira <joaoxsouls@gmail.com>
     Joao Pedro Silva <j.pedro004@gmail.com>
     Joe Heck <http://www.rhonabwy.com/wp/>
+    Joe Jackson <joe@joejackson.me>
     Joel Bohman <mail@jbohman.com>
     Joel Heenan <joelh-django@planetjoel.com>
     Joel Watts <joel@joelwatts.com>
diff --git a/django/db/models/functions/datetime.py b/django/db/models/functions/datetime.py
index b6594b043b..6828980733 100644
--- a/django/db/models/functions/datetime.py
+++ b/django/db/models/functions/datetime.py
@@ -292,7 +292,7 @@ class TruncDate(TruncBase):
     def as_sql(self, compiler, connection):
         # Cast to date rather than truncate to date.
         lhs, lhs_params = compiler.compile(self.lhs)
-        tzname = timezone.get_current_timezone_name() if settings.USE_TZ else None
+        tzname = self.get_tzname()
         sql = connection.ops.datetime_cast_date_sql(lhs, tzname)
         return sql, lhs_params
 
@@ -305,7 +305,7 @@ class TruncTime(TruncBase):
     def as_sql(self, compiler, connection):
         # Cast to time rather than truncate to time.
         lhs, lhs_params = compiler.compile(self.lhs)
-        tzname = timezone.get_current_timezone_name() if settings.USE_TZ else None
+        tzname = self.get_tzname()
         sql = connection.ops.datetime_cast_time_sql(lhs, tzname)
         return sql, lhs_params
 
diff --git a/docs/ref/models/database-functions.txt b/docs/ref/models/database-functions.txt
index f5efdb7e87..3121a36fa9 100644
--- a/docs/ref/models/database-functions.txt
+++ b/docs/ref/models/database-functions.txt
@@ -623,20 +623,28 @@ that deal with date-parts can be used with ``DateField``::
 ``DateTimeField`` truncation
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-.. class:: TruncDate(expression, **extra)
+.. class:: TruncDate(expression, tzinfo=None, **extra)
 
     .. attribute:: lookup_name = 'date'
     .. attribute:: output_field = DateField()
 
+    .. versionchanged:: 3.2
+
+        The ``tzinfo`` parameter was added.
+
 ``TruncDate`` casts ``expression`` to a date rather than using the built-in SQL
 truncate function. It's also registered as a transform on  ``DateTimeField`` as
 ``__date``.
 
-.. class:: TruncTime(expression, **extra)
+.. class:: TruncTime(expression, tzinfo=None, **extra)
 
     .. attribute:: lookup_name = 'time'
     .. attribute:: output_field = TimeField()
 
+    .. versionchanged:: 3.2
+
+        The ``tzinfo`` parameter was added.
+
 ``TruncTime`` casts ``expression`` to a time rather than using the built-in SQL
 truncate function. It's also registered as a transform on ``DateTimeField`` as
 ``__time``.
diff --git a/docs/releases/3.2.txt b/docs/releases/3.2.txt
index d29a582d74..9017c33138 100644
--- a/docs/releases/3.2.txt
+++ b/docs/releases/3.2.txt
@@ -290,6 +290,11 @@ Models
   distinct fields if there's only one field specified in
   :meth:`.QuerySet.distinct`.
 
+* The new ``tzinfo`` parameter of the
+  :class:`~django.db.models.functions.TruncDate` and
+  :class:`~django.db.models.functions.TruncTime` database functions allows
+  truncating datetimes in a specific timezone.
+
 Pagination
 ~~~~~~~~~~
 
diff --git a/tests/db_functions/datetime/test_extract_trunc.py b/tests/db_functions/datetime/test_extract_trunc.py
index f8ebb81cb5..f898ba5253 100644
--- a/tests/db_functions/datetime/test_extract_trunc.py
+++ b/tests/db_functions/datetime/test_extract_trunc.py
@@ -1124,14 +1124,24 @@ class DateFunctionWithTimeZoneTests(DateFunctionTests):
         model = DTModel.objects.annotate(
             melb_year=TruncYear('start_datetime', tzinfo=melb),
             pacific_year=TruncYear('start_datetime', tzinfo=pacific),
+            melb_date=TruncDate('start_datetime', tzinfo=melb),
+            pacific_date=TruncDate('start_datetime', tzinfo=pacific),
+            melb_time=TruncTime('start_datetime', tzinfo=melb),
+            pacific_time=TruncTime('start_datetime', tzinfo=pacific),
         ).order_by('start_datetime').get()
 
+        melb_start_datetime = start_datetime.astimezone(melb)
+        pacific_start_datetime = start_datetime.astimezone(pacific)
         self.assertEqual(model.start_datetime, start_datetime)
         self.assertEqual(model.melb_year, truncate_to(start_datetime, 'year', melb))
         self.assertEqual(model.pacific_year, truncate_to(start_datetime, 'year', pacific))
         self.assertEqual(model.start_datetime.year, 2016)
         self.assertEqual(model.melb_year.year, 2016)
         self.assertEqual(model.pacific_year.year, 2015)
+        self.assertEqual(model.melb_date, melb_start_datetime.date())
+        self.assertEqual(model.pacific_date, pacific_start_datetime.date())
+        self.assertEqual(model.melb_time, melb_start_datetime.time())
+        self.assertEqual(model.pacific_time, pacific_start_datetime.time())
 
     def test_trunc_ambiguous_and_invalid_times(self):
         sao = pytz.timezone('America/Sao_Paulo')