diff --git a/pkg/controller/job/indexed_job_utils.go b/pkg/controller/job/indexed_job_utils.go
index 9ec8f8535b2..0778e60ba58 100644
--- a/pkg/controller/job/indexed_job_utils.go
+++ b/pkg/controller/job/indexed_job_utils.go
@@ -315,7 +315,8 @@ func addCompletionIndexLabel(template *v1.PodTemplateSpec, index int) {
 	if template.Labels == nil {
 		template.Labels = make(map[string]string, 1)
 	}
-	template.Labels[batch.JobCompletionIndexLabel] = strconv.Itoa(index)
+	// For consistency, we use the annotation batch.kubernetes.io/job-completion-index for the corresponding label as well.
+	template.Labels[batch.JobCompletionIndexAnnotation] = strconv.Itoa(index)
 }
 
 func podGenerateNameWithIndex(jobName string, index int) string {
diff --git a/pkg/controller/job/job_controller_test.go b/pkg/controller/job/job_controller_test.go
index e3b71aa68d9..c9c147c6e41 100644
--- a/pkg/controller/job/job_controller_test.go
+++ b/pkg/controller/job/job_controller_test.go
@@ -4413,8 +4413,8 @@ func TestFinalizersRemovedExpectations(t *testing.T) {
 func checkJobCompletionLabel(t *testing.T, p *v1.PodTemplateSpec) {
 	t.Helper()
 	labels := p.GetLabels()
-	if labels == nil || labels[batch.JobCompletionIndexLabel] == "" {
-		t.Errorf("missing expected pod label %s", batch.JobCompletionIndexLabel)
+	if labels == nil || labels[batch.JobCompletionIndexAnnotation] == "" {
+		t.Errorf("missing expected pod label %s", batch.JobCompletionIndexAnnotation)
 	}
 }
 
diff --git a/staging/src/k8s.io/api/apps/v1/types.go b/staging/src/k8s.io/api/apps/v1/types.go
index 15dc3150a63..c3f5a6e21c3 100644
--- a/staging/src/k8s.io/api/apps/v1/types.go
+++ b/staging/src/k8s.io/api/apps/v1/types.go
@@ -17,7 +17,7 @@ limitations under the License.
 package v1
 
 import (
-	"k8s.io/api/core/v1"
+	v1 "k8s.io/api/core/v1"
 	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
 	runtime "k8s.io/apimachinery/pkg/runtime"
 	"k8s.io/apimachinery/pkg/util/intstr"
@@ -29,6 +29,7 @@ const (
 	DeprecatedRollbackTo           = "deprecated.deployment.rollback.to"
 	DeprecatedTemplateGeneration   = "deprecated.daemonset.template.generation"
 	StatefulSetPodNameLabel        = "statefulset.kubernetes.io/pod-name"
+	StatefulSetPodIndexLabel       = "statefulset.kubernetes.io/pod-index"
 )
 
 // +genclient
diff --git a/staging/src/k8s.io/api/batch/v1/types.go b/staging/src/k8s.io/api/batch/v1/types.go
index 15cc874ff21..22cf9ee9cb6 100644
--- a/staging/src/k8s.io/api/batch/v1/types.go
+++ b/staging/src/k8s.io/api/batch/v1/types.go
@@ -28,8 +28,6 @@ const (
 	labelPrefix = "batch.kubernetes.io/"
 
 	JobCompletionIndexAnnotation = labelPrefix + "job-completion-index"
-	// JobCompletionIndexLabel is defined following the format <controller>.kubernetes.io/pod-index
-	JobCompletionIndexLabel = "job.kubernetes.io/pod-index"
 	// JobTrackingFinalizer is a finalizer for Job's pods. It prevents them from
 	// being deleted before being accounted in the Job status.
 	//