diff --git a/muted-tests.yml b/muted-tests.yml
index 7f5f71881557d..84c564acc464c 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -513,8 +513,6 @@ tests:
 - class: org.elasticsearch.xpack.transform.checkpoint.TransformCCSCanMatchIT
   method: testTransformLifecycle_RangeQueryThatMatchesNoShards
   issue: https://github.com/elastic/elasticsearch/issues/121480
-- class: org.elasticsearch.xpack.migrate.action.ReindexDatastreamIndexTransportActionIT
-  issue: https://github.com/elastic/elasticsearch/issues/121737
 - class: org.elasticsearch.xpack.security.authc.service.ServiceAccountSingleNodeTests
   method: testAuthenticateWithServiceFileToken
   issue: https://github.com/elastic/elasticsearch/issues/120988
diff --git a/x-pack/plugin/migrate/src/internalClusterTest/java/org/elasticsearch/xpack/migrate/action/ReindexDatastreamIndexTransportActionIT.java b/x-pack/plugin/migrate/src/internalClusterTest/java/org/elasticsearch/xpack/migrate/action/ReindexDatastreamIndexTransportActionIT.java
index af9269072ef85..06edc94849ab2 100644
--- a/x-pack/plugin/migrate/src/internalClusterTest/java/org/elasticsearch/xpack/migrate/action/ReindexDatastreamIndexTransportActionIT.java
+++ b/x-pack/plugin/migrate/src/internalClusterTest/java/org/elasticsearch/xpack/migrate/action/ReindexDatastreamIndexTransportActionIT.java
@@ -26,6 +26,8 @@
 import org.elasticsearch.action.index.IndexRequest;
 import org.elasticsearch.action.ingest.DeletePipelineRequest;
 import org.elasticsearch.action.ingest.DeletePipelineTransportAction;
+import org.elasticsearch.action.ingest.GetPipelineAction;
+import org.elasticsearch.action.ingest.GetPipelineRequest;
 import org.elasticsearch.action.ingest.PutPipelineRequest;
 import org.elasticsearch.action.ingest.PutPipelineTransportAction;
 import org.elasticsearch.cluster.block.ClusterBlockException;
@@ -51,7 +53,7 @@
 import org.elasticsearch.xcontent.XContentType;
 import org.elasticsearch.xpack.migrate.MigratePlugin;
 import org.elasticsearch.xpack.migrate.MigrateTemplateRegistry;
-import org.junit.After;
+import org.junit.Before;
 
 import java.io.IOException;
 import java.time.Instant;
@@ -69,14 +71,26 @@
 import static org.hamcrest.Matchers.equalTo;
 
 public class ReindexDatastreamIndexTransportActionIT extends ESIntegTestCase {
-    @After
-    private void cleanup() {
+
+    @Before
+    private void setup() throws Exception {
         safeGet(
             clusterAdmin().execute(
                 DeletePipelineTransportAction.TYPE,
                 new DeletePipelineRequest(MigrateTemplateRegistry.REINDEX_DATA_STREAM_PIPELINE_NAME)
             )
         );
+
+        assertBusy(() -> {
+            assertTrue(
+                safeGet(
+                    clusterAdmin().execute(
+                        GetPipelineAction.INSTANCE,
+                        new GetPipelineRequest(MigrateTemplateRegistry.REINDEX_DATA_STREAM_PIPELINE_NAME)
+                    )
+                ).isFound()
+            );
+        });
     }
 
     private static final String MAPPING = """
@@ -121,6 +135,9 @@ public void testTimestamp0AddedIfMissing() {
         // add doc without timestamp
         addDoc(sourceIndex, "{\"foo\":\"baz\"}");
 
+        // wait until doc is written to all shards before adding mapping
+        ensureHealth(sourceIndex);
+
         // add timestamp to source mapping
         indicesAdmin().preparePutMapping(sourceIndex).setSource(DATA_STREAM_MAPPING, XContentType.JSON).get();
 
@@ -136,6 +153,7 @@ public void testTimestamp0AddedIfMissing() {
     }
 
     public void testTimestampNotAddedIfExists() {
+
         var sourceIndex = randomAlphaOfLength(20).toLowerCase(Locale.ROOT);
         safeGet(indicesAdmin().create(new CreateIndexRequest(sourceIndex)));
 
@@ -144,6 +162,9 @@ public void testTimestampNotAddedIfExists() {
         var doc = String.format(Locale.ROOT, "{\"%s\":\"%s\"}", DEFAULT_TIMESTAMP_FIELD, time);
         addDoc(sourceIndex, doc);
 
+        // wait until doc is written to all shards before adding mapping
+        ensureHealth(sourceIndex);
+
         // add timestamp to source mapping
         indicesAdmin().preparePutMapping(sourceIndex).setSource(DATA_STREAM_MAPPING, XContentType.JSON).get();
 
@@ -189,6 +210,9 @@ public void testCustomReindexPipeline() {
         var doc = String.format(Locale.ROOT, "{\"%s\":\"%s\"}", DEFAULT_TIMESTAMP_FIELD, time);
         addDoc(sourceIndex, doc);
 
+        // wait until doc is written to all shards before adding mapping
+        ensureHealth(sourceIndex);
+
         // add timestamp to source mapping
         indicesAdmin().preparePutMapping(sourceIndex).setSource(DATA_STREAM_MAPPING, XContentType.JSON).get();
 
@@ -298,7 +322,7 @@ public void testMissingSourceIndex() {
         );
     }
 
-    public void testSettingsAddedBeforeReindex() throws Exception {
+    public void testSettingsAddedBeforeReindex() {
         // start with a static setting
         var numShards = randomIntBetween(1, 10);
         var staticSettings = Settings.builder().put(IndexMetadata.SETTING_NUMBER_OF_SHARDS, numShards).build();
@@ -603,4 +627,12 @@ void addDoc(String index, String doc) {
         bulkRequest.add(new IndexRequest(index).opType(DocWriteRequest.OpType.CREATE).source(doc, XContentType.JSON));
         safeGet(client().bulk(bulkRequest));
     }
+
+    private void ensureHealth(String index) {
+        if (cluster().numDataNodes() > 1) {
+            ensureGreen(index);
+        } else {
+            ensureYellow(index);
+        }
+    }
 }