diff --git a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/MlConfigMigrator.java b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/MlConfigMigrator.java
index f497a6c7063fe..28e6f34cd9e3f 100644
--- a/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/MlConfigMigrator.java
+++ b/x-pack/plugin/ml/src/main/java/org/elasticsearch/xpack/ml/MlConfigMigrator.java
@@ -33,6 +33,7 @@
 import org.elasticsearch.common.xcontent.XContentBuilder;
 import org.elasticsearch.common.xcontent.XContentFactory;
 import org.elasticsearch.index.IndexSettings;
+import org.elasticsearch.index.engine.VersionConflictEngineException;
 import org.elasticsearch.persistent.PersistentTasksCustomMetaData;
 import org.elasticsearch.xpack.core.ml.MlMetadata;
 import org.elasticsearch.xpack.core.ml.MlTasks;
@@ -369,7 +370,14 @@ public void snapshotMlMeta(MlMetadata mlMetadata, ActionListener<Boolean> listen
                         indexResponse -> {
                             listener.onResponse(indexResponse.getResult() == DocWriteResponse.Result.CREATED);
                         },
-                        listener::onFailure),
+                        e -> {
+                            if (e instanceof VersionConflictEngineException) {
+                                // the snapshot already exists
+                                listener.onResponse(Boolean.TRUE);
+                            } else {
+                                listener.onFailure(e);
+                            }
+                        }),
                 client::index
         );
     }
diff --git a/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/integration/MlConfigMigratorIT.java b/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/integration/MlConfigMigratorIT.java
index 87c0e4ac824ce..55e8dc163dc4d 100644
--- a/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/integration/MlConfigMigratorIT.java
+++ b/x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/integration/MlConfigMigratorIT.java
@@ -6,8 +6,11 @@
 package org.elasticsearch.xpack.ml.integration;
 
 import org.elasticsearch.Version;
+import org.elasticsearch.action.DocWriteRequest;
 import org.elasticsearch.action.get.GetResponse;
+import org.elasticsearch.action.index.IndexRequestBuilder;
 import org.elasticsearch.action.index.IndexResponse;
+import org.elasticsearch.action.support.WriteRequest;
 import org.elasticsearch.cluster.ClusterName;
 import org.elasticsearch.cluster.ClusterState;
 import org.elasticsearch.cluster.ClusterStateUpdateTask;
@@ -178,6 +181,59 @@ public void testMigrateConfigs() throws InterruptedException, IOException {
         assertEquals("df-1", datafeedsHolder.get().get(0).getId());
     }
 
+    public void testExistingSnapshotDoesNotBlockMigration() throws InterruptedException {
+        // index a doc with the same Id as the config snapshot
+        IndexRequestBuilder indexRequest = client().prepareIndex(AnomalyDetectorsIndex.jobStateIndexName(),
+                ElasticsearchMappings.DOC_TYPE, "ml-config")
+                .setSource(Collections.singletonMap("a_field", "a_value"))
+                .setOpType(DocWriteRequest.OpType.CREATE)
+                .setRefreshPolicy(WriteRequest.RefreshPolicy.IMMEDIATE);
+
+        indexRequest.execute().actionGet();
+
+        // define the configs
+        MlMetadata.Builder mlMetadata = new MlMetadata.Builder();
+        mlMetadata.putJob(buildJobBuilder("job-foo").build(), false);
+
+        MetaData.Builder metaData = MetaData.builder();
+        RoutingTable.Builder routingTable = RoutingTable.builder();
+        addMlConfigIndex(metaData, routingTable);
+        ClusterState clusterState = ClusterState.builder(new ClusterName("_name"))
+                .metaData(metaData.putCustom(MlMetadata.TYPE, mlMetadata.build()))
+                .routingTable(routingTable.build())
+                .build();
+
+        doAnswer(invocation -> {
+            ClusterStateUpdateTask listener = (ClusterStateUpdateTask) invocation.getArguments()[1];
+            listener.clusterStateProcessed("source", mock(ClusterState.class), mock(ClusterState.class));
+            return null;
+        }).when(clusterService).submitStateUpdateTask(eq("remove-migrated-ml-configs"), any());
+
+        AtomicReference<Exception> exceptionHolder = new AtomicReference<>();
+        AtomicReference<Boolean> responseHolder = new AtomicReference<>();
+
+        // do the migration
+        MlConfigMigrator mlConfigMigrator = new MlConfigMigrator(nodeSettings(), client(), clusterService);
+        // writing the snapshot should fail because the doc already exists
+        // in which case the migration should continue
+        blockingCall(actionListener -> mlConfigMigrator.migrateConfigsWithoutTasks(clusterState, actionListener),
+                responseHolder, exceptionHolder);
+
+        assertNull(exceptionHolder.get());
+        assertTrue(responseHolder.get());
+
+        // check the jobs have been migrated
+        AtomicReference<List<Job.Builder>> jobsHolder = new AtomicReference<>();
+        JobConfigProvider jobConfigProvider = new JobConfigProvider(client());
+        blockingCall(actionListener -> jobConfigProvider.expandJobs("*", true, true, actionListener),
+                jobsHolder, exceptionHolder);
+
+        assertNull(exceptionHolder.get());
+        assertThat(jobsHolder.get(), hasSize(1));
+        assertTrue(jobsHolder.get().get(0).build().getCustomSettings().containsKey(MlConfigMigrator.MIGRATED_FROM_VERSION));
+        assertEquals("job-foo", jobsHolder.get().get(0).build().getId());
+    }
+
     public void testMigrateConfigs_GivenLargeNumberOfJobsAndDatafeeds() throws InterruptedException {
         int jobCount = randomIntBetween(150, 201);
         int datafeedCount = randomIntBetween(150, jobCount);