diff --git a/internal/base/base.go b/internal/base/base.go
index 4e7186c..5b0023b 100644
--- a/internal/base/base.go
+++ b/internal/base/base.go
@@ -48,6 +48,7 @@ const (
 	TaskStateScheduled
 	TaskStateRetry
 	TaskStateArchived
+	TaskStateCompleted
 )
 
 func (s TaskState) String() string {
@@ -62,6 +63,8 @@ func (s TaskState) String() string {
 		return "retry"
 	case TaskStateArchived:
 		return "archived"
+	case TaskStateCompleted:
+		return "completed"
 	}
 	panic(fmt.Sprintf("internal error: unknown task state %d", s))
 }
@@ -78,6 +81,8 @@ func TaskStateFromString(s string) (TaskState, error) {
 		return TaskStateRetry, nil
 	case "archived":
 		return TaskStateArchived, nil
+	case "completed":
+		return TaskStateCompleted, nil
 	}
 	return 0, errors.E(errors.FailedPrecondition, fmt.Sprintf("%q is not supported task state", s))
 }
@@ -136,6 +141,10 @@ func DeadlinesKey(qname string) string {
 	return fmt.Sprintf("%sdeadlines", QueueKeyPrefix(qname))
 }
 
+func CompletedKey(qname string) string {
+	return fmt.Sprintf("%scompleted", QueueKeyPrefix(qname))
+}
+
 // PausedKey returns a redis key to indicate that the given queue is paused.
 func PausedKey(qname string) string {
 	return fmt.Sprintf("%spaused", QueueKeyPrefix(qname))
diff --git a/internal/base/base_test.go b/internal/base/base_test.go
index 7da6cc5..f49d336 100644
--- a/internal/base/base_test.go
+++ b/internal/base/base_test.go
@@ -139,6 +139,23 @@ func TestArchivedKey(t *testing.T) {
 	}
 }
 
+func TestCompletedKey(t *testing.T) {
+	tests := []struct {
+		qname string
+		want  string
+	}{
+		{"default", "asynq:{default}:completed"},
+		{"custom", "asynq:{custom}:completed"},
+	}
+
+	for _, tc := range tests {
+		got := CompletedKey(tc.qname)
+		if got != tc.want {
+			t.Errorf("CompletedKey(%q) = %q, want %q", tc.qname, got, tc.want)
+		}
+	}
+}
+
 func TestPausedKey(t *testing.T) {
 	tests := []struct {
 		qname string