diff --git a/internal/services/machinelearning/machine_learning_compute_cluster_resource.go b/internal/services/machinelearning/machine_learning_compute_cluster_resource.go
index 28a28518c29a..aea83b485cb8 100644
--- a/internal/services/machinelearning/machine_learning_compute_cluster_resource.go
+++ b/internal/services/machinelearning/machine_learning_compute_cluster_resource.go
@@ -27,6 +27,7 @@ func resourceComputeCluster() *pluginsdk.Resource {
 	return &pluginsdk.Resource{
 		Create: resourceComputeClusterCreate,
 		Read:   resourceComputeClusterRead,
+		Update: resourceComputeClusterUpdate,
 		Delete: resourceComputeClusterDelete,
 
 		Importer: pluginsdk.ImporterValidatingResourceId(func(id string) error {
@@ -37,6 +38,7 @@ func resourceComputeCluster() *pluginsdk.Resource {
 		Timeouts: &pluginsdk.ResourceTimeout{
 			Create: pluginsdk.DefaultTimeout(30 * time.Minute),
 			Read:   pluginsdk.DefaultTimeout(5 * time.Minute),
+			Update: pluginsdk.DefaultTimeout(30 * time.Minute),
 			Delete: pluginsdk.DefaultTimeout(30 * time.Minute),
 		},
 
@@ -69,7 +71,7 @@ func resourceComputeCluster() *pluginsdk.Resource {
 				ValidateFunc: validation.StringInSlice([]string{string(machinelearningcomputes.VMPriorityDedicated), string(machinelearningcomputes.VMPriorityLowPriority)}, false),
 			},
 
-			"identity": commonschema.SystemAssignedUserAssignedIdentityOptionalForceNew(),
+			"identity": commonschema.SystemAssignedUserAssignedIdentityOptional(),
 
 			"scale_settings": {
 				Type:     pluginsdk.TypeList,
@@ -355,6 +357,36 @@ func resourceComputeClusterRead(d *pluginsdk.ResourceData, meta interface{}) err
 	return tags.FlattenAndSet(d, computeResource.Model.Tags)
 }
 
+func resourceComputeClusterUpdate(d *pluginsdk.ResourceData, meta interface{}) error {
+	client := meta.(*clients.Client).MachineLearning.MachineLearningComputes
+	ctx, cancel := timeouts.ForCreate(meta.(*clients.Client).StopContext, d)
+	defer cancel()
+
+	id, err := machinelearningcomputes.ParseComputeID(d.Id())
+	if err != nil {
+		return err
+	}
+
+	existing, err := client.ComputeGet(ctx, *id)
+	if err != nil {
+		return fmt.Errorf("retrieving %s: %+v", *id, err)
+	}
+	payload := existing.Model
+	if payload == nil {
+		return fmt.Errorf("retrieving %s: `model` was nil", *id)
+	}
+	identity, err := expandIdentity(d.Get("identity").([]interface{}))
+	if err != nil {
+		return fmt.Errorf("expanding `identity`: %+v", err)
+	}
+	payload.Identity = identity
+	if err := client.ComputeCreateOrUpdateThenPoll(ctx, *id, *payload); err != nil {
+		return fmt.Errorf("updating %s: %+v", id, err)
+	}
+
+	return resourceComputeClusterRead(d, meta)
+}
+
 func resourceComputeClusterDelete(d *pluginsdk.ResourceData, meta interface{}) error {
 	client := meta.(*clients.Client).MachineLearning.MachineLearningComputes
 	ctx, cancel := timeouts.ForDelete(meta.(*clients.Client).StopContext, d)
diff --git a/internal/services/machinelearning/machine_learning_compute_cluster_resource_test.go b/internal/services/machinelearning/machine_learning_compute_cluster_resource_test.go
index 66a004d6ba61..461babfcd37b 100644
--- a/internal/services/machinelearning/machine_learning_compute_cluster_resource_test.go
+++ b/internal/services/machinelearning/machine_learning_compute_cluster_resource_test.go
@@ -178,7 +178,6 @@ resource "azurerm_machine_learning_compute_cluster" "test" {
   vm_priority                   = "LowPriority"
   vm_size                       = "STANDARD_DS2_V2"
   machine_learning_workspace_id = azurerm_machine_learning_workspace.test.id
-  local_auth_enabled            = false
 
   scale_settings {
     min_node_count                       = 0
@@ -318,6 +317,7 @@ resource "azurerm_user_assigned_identity" "test" {
   location            = azurerm_resource_group.test.location
   resource_group_name = azurerm_resource_group.test.name
 }
+
 resource "azurerm_machine_learning_compute_cluster" "test" {
   name                          = "CC-%d"
   location                      = azurerm_resource_group.test.location
@@ -343,22 +343,26 @@ func (r ComputeClusterResource) identitySystemAssignedUserAssigned(data acceptan
 	template := r.template_basic(data)
 	return fmt.Sprintf(`
 %s
+
 resource "azurerm_user_assigned_identity" "test" {
   name                = "acctestUAI-%d"
   location            = azurerm_resource_group.test.location
   resource_group_name = azurerm_resource_group.test.name
 }
+
 resource "azurerm_machine_learning_compute_cluster" "test" {
-  name                          = "CC-%d"
-  location                      = azurerm_resource_group.test.location
-  vm_priority                   = "LowPriority"
-  vm_size                       = "STANDARD_DS2_V2"
+  name        = "CC-%d"
+  location    = azurerm_resource_group.test.location
+  vm_priority = "LowPriority"
+  vm_size     = "STANDARD_DS2_V2"
+
   machine_learning_workspace_id = azurerm_machine_learning_workspace.test.id
   scale_settings {
     min_node_count                       = 0
     max_node_count                       = 1
     scale_down_nodes_after_idle_duration = "PT30S" # 30 seconds
   }
+
   identity {
     type = "SystemAssigned, UserAssigned"
     identity_ids = [
diff --git a/website/docs/r/machine_learning_compute_cluster.html.markdown b/website/docs/r/machine_learning_compute_cluster.html.markdown
index f694ed67fff2..1128e7057462 100644
--- a/website/docs/r/machine_learning_compute_cluster.html.markdown
+++ b/website/docs/r/machine_learning_compute_cluster.html.markdown
@@ -119,7 +119,7 @@ The following arguments are supported:
 
 * `description` - (Optional) The description of the Machine Learning compute. Changing this forces a new Machine Learning Compute Cluster to be created.
 
-* `identity` - (Optional) An `identity` block as defined below. Changing this forces a new Machine Learning Compute Cluster to be created.
+* `identity` - (Optional) An `identity` block as defined below.
 
 * `local_auth_enabled` - (Optional) Whether local authentication methods is enabled. Defaults to `true`. Changing this forces a new Machine Learning Compute Cluster to be created.