diff --git a/sdk/eventhub/event-hubs/CHANGELOG.md b/sdk/eventhub/event-hubs/CHANGELOG.md
index 734809f546af..520ec2c9b68c 100644
--- a/sdk/eventhub/event-hubs/CHANGELOG.md
+++ b/sdk/eventhub/event-hubs/CHANGELOG.md
@@ -6,6 +6,12 @@
   where events could be _skipped_ while receiving messages.
   Previously this could occur when a retryable error was encountered and retries were exhausted while receiving a batch of events.
 
+### Tracing updates:
+
+- Addresses [#10276](https://github.com/Azure/azure-sdk-for-js/issues/10276): adds
+  `message_bus.destination` and `peer.address` attributes to `Azure.EventHubs.message` spans.
+  ([PR 10389](https://github.com/Azure/azure-sdk-for-js/pull/10389))
+
 ## 5.3.0-preview.1 (2020-07-07)
 
 - Adds `loadBalancingOptions` to the `EventHubConsumerClient` to add control around
diff --git a/sdk/eventhub/event-hubs/src/diagnostics/messageSpan.ts b/sdk/eventhub/event-hubs/src/diagnostics/messageSpan.ts
index 15ca481c5964..ad15fae72bbc 100644
--- a/sdk/eventhub/event-hubs/src/diagnostics/messageSpan.ts
+++ b/sdk/eventhub/event-hubs/src/diagnostics/messageSpan.ts
@@ -3,18 +3,26 @@
 
 import { getTracer } from "@azure/core-tracing";
 import { Span, SpanContext, SpanKind } from "@opentelemetry/api";
+import { EventHubConnectionConfig } from "@azure/core-amqp";
 
 /**
  * @internal
  * @ignore
  */
-export function createMessageSpan(parentSpan?: Span | SpanContext | null): Span {
+export function createMessageSpan(
+  parentSpan?: Span | SpanContext | null,
+  eventHubConfig?: Pick<EventHubConnectionConfig, "entityPath" | "host">
+): Span {
   const tracer = getTracer();
   const span = tracer.startSpan("Azure.EventHubs.message", {
     kind: SpanKind.PRODUCER,
     parent: parentSpan
   });
   span.setAttribute("az.namespace", "Microsoft.EventHub");
+  if (eventHubConfig) {
+    span.setAttribute("message_bus.destination", eventHubConfig.entityPath);
+    span.setAttribute("peer.address", eventHubConfig.host);
+  }
 
   return span;
 }
diff --git a/sdk/eventhub/event-hubs/src/eventDataBatch.ts b/sdk/eventhub/event-hubs/src/eventDataBatch.ts
index 5299b3370519..eca16b5b6826 100644
--- a/sdk/eventhub/event-hubs/src/eventDataBatch.ts
+++ b/sdk/eventhub/event-hubs/src/eventDataBatch.ts
@@ -296,7 +296,7 @@ export class EventDataBatchImpl implements EventDataBatch {
     );
     let spanContext: SpanContext | undefined;
     if (!previouslyInstrumented) {
-      const messageSpan = createMessageSpan(options.parentSpan);
+      const messageSpan = createMessageSpan(options.parentSpan, this._context.config);
       eventData = instrumentEventData(eventData, messageSpan);
       spanContext = messageSpan.context();
       messageSpan.end();
diff --git a/sdk/eventhub/event-hubs/src/eventHubProducerClient.ts b/sdk/eventhub/event-hubs/src/eventHubProducerClient.ts
index 5ef3d55c39f5..7f03604d06fa 100644
--- a/sdk/eventhub/event-hubs/src/eventHubProducerClient.ts
+++ b/sdk/eventhub/event-hubs/src/eventHubProducerClient.ts
@@ -265,7 +265,10 @@ export class EventHubProducerClient {
       for (let i = 0; i < batch.length; i++) {
         const event = batch[i];
         if (!event.properties || !event.properties[TRACEPARENT_PROPERTY]) {
-          const messageSpan = createMessageSpan(getParentSpan(options.tracingOptions));
+          const messageSpan = createMessageSpan(
+            getParentSpan(options.tracingOptions),
+            this._context.config
+          );
           // since these message spans are created from same context as the send span,
           // these message spans don't need to be linked.
           // replace the original event with the instrumented one
diff --git a/sdk/eventhub/event-hubs/test/diagnostics/messageSpan.spec.ts b/sdk/eventhub/event-hubs/test/diagnostics/messageSpan.spec.ts
new file mode 100644
index 000000000000..63f6f52d5807
--- /dev/null
+++ b/sdk/eventhub/event-hubs/test/diagnostics/messageSpan.spec.ts
@@ -0,0 +1,82 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT license.
+
+import chai from "chai";
+import { createMessageSpan } from "../../src/diagnostics/messageSpan";
+import { TraceFlags, SpanContext } from "@opentelemetry/api";
+import { TestTracer, setTracer, getTracer } from "@azure/core-tracing";
+import { EventHubConnectionConfig } from '@azure/core-amqp';
+
+const should = chai.should();
+const assert = chai.assert;
+
+describe("#createMessageSpan()", () => {
+  const origTracer = getTracer();
+
+  before(() => {
+    setTracer(new TestTracer());
+  });
+
+  after(() => {
+    setTracer(origTracer);
+  });
+
+  const mockSpanContext: SpanContext = {
+    traceId: "d4cda95b652f4a1592b449d5929fda1b",
+    spanId: "6e0c63257de34c92",
+    traceFlags: TraceFlags.SAMPLED
+  };
+  const mockEventHubConnectionConfig: Pick<EventHubConnectionConfig, "entityPath" | "host"> = {
+    entityPath: "entity",
+    host: "foo.example.com"
+  };
+
+  it("should create a span without a parent", () => {
+    const span = createMessageSpan();
+
+    should.exist(span);
+    should.exist(span.context().spanId);
+    should.exist(span.context().traceId);
+
+    should.equal((span as any).name, "Azure.EventHubs.message");
+    assert.deepStrictEqual((span as any).attributes, {
+      "az.namespace": "Microsoft.EventHub"
+    });
+
+    span.end();
+  });
+
+  it("should create a span with a parent", () => {
+    const span = createMessageSpan(mockSpanContext);
+
+    should.exist(span);
+    should.equal(span.context().traceId, mockSpanContext.traceId);
+    should.exist(span.context().spanId);
+    should.not.equal(span.context().spanId, mockSpanContext.spanId);
+
+    should.equal((span as any).name, "Azure.EventHubs.message");
+    assert.deepStrictEqual((span as any).attributes, {
+      "az.namespace": "Microsoft.EventHub"
+    });
+
+    span.end();
+  });
+
+  it("should create a span with an eventHubConfig", () => {
+    const span = createMessageSpan(mockSpanContext, mockEventHubConnectionConfig);
+
+    should.exist(span);
+    should.equal(span.context().traceId, mockSpanContext.traceId);
+    should.exist(span.context().spanId);
+    should.not.equal(span.context().spanId, mockSpanContext.spanId);
+
+    should.equal((span as any).name, "Azure.EventHubs.message");
+    assert.deepStrictEqual((span as any).attributes, {
+      "az.namespace": "Microsoft.EventHub",
+      "message_bus.destination": mockEventHubConnectionConfig.entityPath,
+      "peer.address": mockEventHubConnectionConfig.host
+    });
+
+    span.end();
+  });
+});