diff --git a/tokio/src/time/driver/sleep.rs b/tokio/src/time/driver/sleep.rs
index d8173c2524b..5c366293d5f 100644
--- a/tokio/src/time/driver/sleep.rs
+++ b/tokio/src/time/driver/sleep.rs
@@ -58,7 +58,10 @@ pub fn sleep_until(deadline: Instant) -> Sleep {
 // Alias for old name in 0.x
 #[cfg_attr(docsrs, doc(alias = "delay_for"))]
 pub fn sleep(duration: Duration) -> Sleep {
-    sleep_until(Instant::now() + duration)
+    match Instant::now().checked_add(duration) {
+        Some(deadline) => sleep_until(deadline),
+        None => sleep_until(Instant::far_future()),
+    }
 }
 
 pin_project! {
@@ -168,6 +171,10 @@ impl Sleep {
         Sleep { deadline, entry }
     }
 
+    pub(crate) fn far_future() -> Sleep {
+        Self::new_timeout(Instant::far_future())
+    }
+
     /// Returns the instant at which the future will complete.
     pub fn deadline(&self) -> Instant {
         self.deadline
diff --git a/tokio/src/time/instant.rs b/tokio/src/time/instant.rs
index f4d6eacbfa5..1f8e663fe10 100644
--- a/tokio/src/time/instant.rs
+++ b/tokio/src/time/instant.rs
@@ -54,6 +54,14 @@ impl Instant {
         Instant { std }
     }
 
+    pub(crate) fn far_future() -> Instant {
+        // Roughly 30 years from now.
+        // API does not provide a way to obtain max `Instant`
+        // or convert specific date in the future to instant.
+        // 1000 years overflows on macOS, 100 years overflows on FreeBSD.
+        Self::now() + Duration::from_secs(86400 * 365 * 30)
+    }
+
     /// Convert the value into a `std::time::Instant`.
     pub fn into_std(self) -> std::time::Instant {
         self.std
diff --git a/tokio/src/time/timeout.rs b/tokio/src/time/timeout.rs
index 9d15a7205cd..61964ad2426 100644
--- a/tokio/src/time/timeout.rs
+++ b/tokio/src/time/timeout.rs
@@ -49,7 +49,11 @@ pub fn timeout<T>(duration: Duration, future: T) -> Timeout<T>
 where
     T: Future,
 {
-    let delay = Sleep::new_timeout(Instant::now() + duration);
+    let deadline = Instant::now().checked_add(duration);
+    let delay = match deadline {
+        Some(deadline) => Sleep::new_timeout(deadline),
+        None => Sleep::far_future(),
+    };
     Timeout::new_with_delay(future, delay)
 }
 
diff --git a/tokio/tests/time_timeout.rs b/tokio/tests/time_timeout.rs
index 4efcd8ca82f..dbd80eb8a6a 100644
--- a/tokio/tests/time_timeout.rs
+++ b/tokio/tests/time_timeout.rs
@@ -74,6 +74,33 @@ async fn future_and_timeout_in_future() {
     assert_ready_ok!(fut.poll()).unwrap();
 }
 
+#[tokio::test]
+async fn very_large_timeout() {
+    time::pause();
+
+    // Not yet complete
+    let (tx, rx) = oneshot::channel();
+
+    // copy-paste unstable `Duration::MAX`
+    let duration_max = Duration::from_secs(u64::MAX) + Duration::from_nanos(999_999_999);
+
+    // Wrap it with a deadline
+    let mut fut = task::spawn(timeout(duration_max, rx));
+
+    // Ready!
+    assert_pending!(fut.poll());
+
+    // Turn the timer, it runs for the elapsed time
+    time::advance(Duration::from_secs(86400 * 365 * 10)).await;
+
+    assert_pending!(fut.poll());
+
+    // Complete the future
+    tx.send(()).unwrap();
+
+    assert_ready_ok!(fut.poll()).unwrap();
+}
+
 #[tokio::test]
 async fn deadline_now_elapses() {
     use futures::future::pending;