diff --git a/test/e2e_kubeadm/kubelet_config_test.go b/test/e2e_kubeadm/kubelet_config_test.go
index 7ccc778d360..d109a786cbb 100644
--- a/test/e2e_kubeadm/kubelet_config_test.go
+++ b/test/e2e_kubeadm/kubelet_config_test.go
@@ -17,12 +17,7 @@ limitations under the License.
 package kubeadm
 
 import (
-	"context"
-	"fmt"
-
 	rbacv1 "k8s.io/api/rbac/v1"
-	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
-	"k8s.io/apimachinery/pkg/util/version"
 	"k8s.io/kubernetes/test/e2e/framework"
 	admissionapi "k8s.io/pod-security-admission/api"
 
@@ -38,13 +33,6 @@ var (
 	kubeletConfigConfigMapName   string
 	kubeletConfigRoleName        string
 	kubeletConfigRoleBindingName string
-
-	// TODO: remove these versioned strings and related logic once the UnversionedKubeletConfigMap
-	// feature gate goes GA:
-	// https://github.com/kubernetes/kubeadm/issues/1582
-	kubeletConfigConfigMapNameVersioned   string
-	kubeletConfigRoleNameVersioned        string
-	kubeletConfigRoleBindingNameVersioned string
 )
 
 // Define container for all the test specification aimed at verifying
@@ -68,68 +56,19 @@ var _ = Describe("kubelet-config ConfigMap", func() {
 			return
 		}
 
-		// gets the ClusterConfiguration from the kubeadm kubeadm-config ConfigMap as a untyped map
-		m := getClusterConfiguration(f.ClientSet)
-
-		// Extract the kubernetesVersion
-		// TODO: remove this after the UnversionedKubeletConfigMap feature gate goes GA:
-		// https://github.com/kubernetes/kubeadm/issues/1582
-		// At that point parsing the k8s version will no longer be needed in this test.
-		gomega.Expect(m).To(gomega.HaveKey("kubernetesVersion"))
-		k8sVersionString := m["kubernetesVersion"].(string)
-		k8sVersion, err := version.ParseSemantic(k8sVersionString)
-		if err != nil {
-			framework.Failf("error reading kubernetesVersion from %s ConfigMap: %v", kubeadmConfigName, err)
-		}
-
 		kubeletConfigConfigMapName = "kubelet-config"
 		kubeletConfigRoleName = "kubeadm:kubelet-config"
 		kubeletConfigRoleBindingName = kubeletConfigRoleName
-
-		kubeletConfigConfigMapNameVersioned = fmt.Sprintf("kubelet-config-%d.%d", k8sVersion.Major(), k8sVersion.Minor())
-		kubeletConfigRoleNameVersioned = fmt.Sprintf("kubeadm:kubelet-config-%d.%d", k8sVersion.Major(), k8sVersion.Minor())
-		kubeletConfigRoleBindingNameVersioned = kubeletConfigRoleNameVersioned
 	})
 
 	ginkgo.It("should exist and be properly configured", func() {
-		// TODO: switch to GetConfigMap once UnversionedKubeletConfigMap feature gate goes GA:
-		// https://github.com/kubernetes/kubeadm/issues/1582
-		cm, err := f.ClientSet.CoreV1().
-			ConfigMaps(kubeSystemNamespace).
-			Get(context.TODO(), kubeletConfigConfigMapName, metav1.GetOptions{})
-		if err != nil {
-			cm, err = f.ClientSet.CoreV1().
-				ConfigMaps(kubeSystemNamespace).
-				Get(context.TODO(), kubeletConfigConfigMapNameVersioned, metav1.GetOptions{})
-			framework.ExpectNoError(err, "error getting ConfigMap %q or %q from namespace %q",
-				kubeletConfigConfigMapName, kubeletConfigConfigMapNameVersioned, kubeSystemNamespace)
-		}
+		cm := GetConfigMap(f.ClientSet, kubeSystemNamespace, kubeletConfigConfigMapName)
 		gomega.Expect(cm.Data).To(gomega.HaveKey(kubeletConfigConfigMapKey))
 	})
 
 	ginkgo.It("should have related Role and RoleBinding", func() {
-		// TODO: switch to ExpectRole(Binding) once UnversionedKubeletConfigMap feature gate goes GA:
-		// https://github.com/kubernetes/kubeadm/issues/1582
-		_, err := f.ClientSet.RbacV1().
-			Roles(kubeSystemNamespace).
-			Get(context.TODO(), kubeletConfigRoleName, metav1.GetOptions{})
-		if err != nil {
-			_, err = f.ClientSet.RbacV1().
-				Roles(kubeSystemNamespace).
-				Get(context.TODO(), kubeletConfigRoleNameVersioned, metav1.GetOptions{})
-			framework.ExpectNoError(err, "error getting Role %q or %q from namespace %q",
-				kubeletConfigRoleName, kubeletConfigRoleNameVersioned, kubeSystemNamespace)
-		}
-		_, err = f.ClientSet.RbacV1().
-			Roles(kubeSystemNamespace).
-			Get(context.TODO(), kubeletConfigRoleBindingName, metav1.GetOptions{})
-		if err != nil {
-			_, err = f.ClientSet.RbacV1().
-				Roles(kubeSystemNamespace).
-				Get(context.TODO(), kubeletConfigRoleBindingNameVersioned, metav1.GetOptions{})
-			framework.ExpectNoError(err, "error getting RoleBinding %q or %q from namespace %q",
-				kubeletConfigRoleBindingName, kubeletConfigRoleBindingNameVersioned, kubeSystemNamespace)
-		}
+		ExpectRole(f.ClientSet, kubeSystemNamespace, kubeletConfigRoleName)
+		ExpectRoleBinding(f.ClientSet, kubeSystemNamespace, kubeletConfigRoleBindingName)
 	})
 
 	ginkgo.It("should be accessible for bootstrap tokens", func() {