diff --git a/releasenotes/notes/wait-exponential-jitter-min-timedelta-a8e3c1f4b7d29e50.yaml b/releasenotes/notes/wait-exponential-jitter-min-timedelta-a8e3c1f4b7d29e50.yaml
new file mode 100644
index 00000000..38adcbc6
--- /dev/null
+++ b/releasenotes/notes/wait-exponential-jitter-min-timedelta-a8e3c1f4b7d29e50.yaml
@@ -0,0 +1,6 @@
+---
+features:
+  - |
+    Add ``min`` parameter to ``wait_exponential_jitter`` to set a minimum wait
+    time floor, consistent with ``wait_exponential``. Also accept ``timedelta``
+    for ``max``, ``jitter``, and ``min`` parameters.
diff --git a/tenacity/wait.py b/tenacity/wait.py
index b28b7886..92fa1f4a 100644
--- a/tenacity/wait.py
+++ b/tenacity/wait.py
@@ -240,26 +240,28 @@ def __call__(self, retry_state: "RetryCallState") -> float:
 class wait_exponential_jitter(wait_base):
     """Wait strategy that applies exponential backoff and jitter.
 
-    It allows for a customized initial wait, maximum wait and jitter.
+    It allows for a customized initial wait, maximum wait, jitter and minimum.
 
     This implements the strategy described here:
     https://cloud.google.com/storage/docs/retry-strategy
 
-    The wait time is min(initial * 2**n + random.uniform(0, jitter), maximum)
+    The wait time is max(min, min(initial * 2**n + random.uniform(0, jitter), maximum))
     where n is the retry count.
     """
 
     def __init__(
         self,
         initial: float = 1,
-        max: float = _utils.MAX_WAIT,
+        max: _utils.time_unit_type = _utils.MAX_WAIT,
         exp_base: float = 2,
-        jitter: float = 1,
+        jitter: _utils.time_unit_type = 1,
+        min: _utils.time_unit_type = 0,
     ) -> None:
         self.initial = initial
-        self.max = max
+        self.max = _utils.to_seconds(max)
         self.exp_base = exp_base
-        self.jitter = jitter
+        self.jitter = _utils.to_seconds(jitter)
+        self.min = _utils.to_seconds(min)
 
     def __call__(self, retry_state: "RetryCallState") -> float:
         jitter = random.uniform(0, self.jitter)
@@ -268,4 +270,4 @@ def __call__(self, retry_state: "RetryCallState") -> float:
             result = self.initial * exp + jitter
         except OverflowError:
             result = self.max
-        return max(0, min(result, self.max))
+        return max(max(0, self.min), min(result, self.max))
diff --git a/tests/test_tenacity.py b/tests/test_tenacity.py
index efefba8c..7061cd74 100644
--- a/tests/test_tenacity.py
+++ b/tests/test_tenacity.py
@@ -617,6 +617,29 @@ def test_wait_exponential_jitter(self) -> None:
         fn = tenacity.wait_exponential_jitter()
         fn(make_retry_state(0, 0))
 
+    def test_wait_exponential_jitter_min(self) -> None:
+        fn = tenacity.wait_exponential_jitter(initial=1, max=60, jitter=1, min=5)
+        for _ in range(1000):
+            # Even for attempt 1 (base wait=1 + jitter 0..1 = 1..2), min=5 applies
+            self._assert_inclusive_range(fn(make_retry_state(1, 0)), 5, 5)
+            self._assert_inclusive_range(fn(make_retry_state(2, 0)), 5, 5)
+            self._assert_inclusive_range(fn(make_retry_state(3, 0)), 5, 5)
+            # For attempt 4, base wait=8 + jitter 0..1 = 8..9, above min
+            self._assert_inclusive_range(fn(make_retry_state(4, 0)), 8, 9)
+
+    def test_wait_exponential_jitter_timedelta(self) -> None:
+        from datetime import timedelta
+
+        fn = tenacity.wait_exponential_jitter(
+            max=timedelta(seconds=60),
+            jitter=timedelta(seconds=1),
+            min=timedelta(seconds=5),
+        )
+        for _ in range(1000):
+            self._assert_inclusive_range(fn(make_retry_state(1, 0)), 5, 5)
+            self._assert_inclusive_range(fn(make_retry_state(5, 0)), 16, 17)
+            self.assertEqual(fn(make_retry_state(7, 0)), 60)
+
     def test_wait_retry_state_attributes(self) -> None:
         class ExtractCallState(Exception):
             pass