diff --git a/.chloggen/goleak_datadogconnector.yaml b/.chloggen/goleak_datadogconnector.yaml
new file mode 100755
index 000000000000..4bc8446f564d
--- /dev/null
+++ b/.chloggen/goleak_datadogconnector.yaml
@@ -0,0 +1,27 @@
+# Use this changelog template to create an entry for release notes.
+
+# One of 'breaking', 'deprecation', 'new_component', 'enhancement', 'bug_fix'
+change_type: bug_fix
+
+# The name of the component, or a single word describing the area of concern, (e.g. filelogreceiver)
+component: datadogconnector
+
+# A brief description of the change.  Surround your text with quotes ("") if it needs to start with a backtick (`).
+note: Fix memory leaks
+
+# Mandatory: One or more tracking issues related to the change. You can use the PR number here if no issue exists.
+issues: [30438]
+
+# (Optional) One or more lines of additional information to render under the primary note.
+# These lines will be padded with 2 spaces and then inserted directly into the document.
+# Use pipe (|) for multiline entries.
+subtext:
+
+# If your change doesn't affect end users or the exported elements of any package,
+# you should instead start your pull request title with [chore] or use the "Skip Changelog" label.
+# Optional: The change log or logs in which this entry should be included.
+# e.g. '[user]' or '[user, api]'
+# Include 'user' if the change is relevant to end users.
+# Include 'api' if there is a change to a library API.
+# Default: '[user]'
+change_logs: []
diff --git a/connector/datadogconnector/connector_test.go b/connector/datadogconnector/connector_test.go
index d5410720be71..5dae71c601bc 100644
--- a/connector/datadogconnector/connector_test.go
+++ b/connector/datadogconnector/connector_test.go
@@ -28,10 +28,12 @@ func TestNewConnector(t *testing.T) {
 
 	_, ok := traceToMetricsConnector.(*connectorImp)
 	assert.True(t, ok) // checks if the created connector implements the connectorImp struct
+	assert.NoError(t, traceToMetricsConnector.Shutdown(context.Background()))
 
 	traceToTracesConnector, err := factory.CreateTracesToTraces(context.Background(), creationParams, cfg, consumertest.NewNop())
 	assert.NoError(t, err)
 
 	_, ok = traceToTracesConnector.(*connectorImp)
 	assert.True(t, ok) // checks if the created connector implements the connectorImp struct
+	assert.NoError(t, traceToTracesConnector.Shutdown(context.Background()))
 }
diff --git a/connector/datadogconnector/go.mod b/connector/datadogconnector/go.mod
index 638a50471cb1..57fa24a5ee7e 100644
--- a/connector/datadogconnector/go.mod
+++ b/connector/datadogconnector/go.mod
@@ -14,6 +14,7 @@ require (
 	go.opentelemetry.io/collector/pdata v1.0.2-0.20240112172857-83d463ceba06
 	go.opentelemetry.io/otel/metric v1.21.0
 	go.opentelemetry.io/otel/trace v1.21.0
+	go.uber.org/goleak v1.3.0
 	go.uber.org/zap v1.26.0
 )
 
diff --git a/connector/datadogconnector/go.sum b/connector/datadogconnector/go.sum
index 68eceac8d97b..d2953266077c 100644
--- a/connector/datadogconnector/go.sum
+++ b/connector/datadogconnector/go.sum
@@ -399,6 +399,7 @@ go.uber.org/atomic v1.9.0/go.mod h1:fEN4uk6kAWBTFdckzkM89CLk9XfWZrxpCo0nPH17wJc=
 go.uber.org/atomic v1.11.0 h1:ZvwS0R+56ePWxUNi+Atn9dWONBPp/AUETXlHW0DxSjE=
 go.uber.org/atomic v1.11.0/go.mod h1:LUxbIzbOniOlMKjJjyPfpl4v+PKK2cNJn91OQbhoJI0=
 go.uber.org/goleak v1.3.0 h1:2K3zAYmnTNqV73imy9J1T3WC+gmCePx2hEGkimedGto=
+go.uber.org/goleak v1.3.0/go.mod h1:CoHD4mav9JJNrW/WLlf7HGZPjdw8EucARQHekz1X6bE=
 go.uber.org/multierr v1.11.0 h1:blXXJkSxSSfBVBlC76pxqeO+LN3aDfLQo+309xJstO0=
 go.uber.org/multierr v1.11.0/go.mod h1:20+QtiLqy0Nd6FdQB9TLXag12DsQkrbs3htMFfDN80Y=
 go.uber.org/zap v1.26.0 h1:sI7k6L95XOKS281NhVKOFCUNIvv9e0w4BF8N3u+tCRo=
diff --git a/connector/datadogconnector/package_test.go b/connector/datadogconnector/package_test.go
new file mode 100644
index 000000000000..bbb42967e1a8
--- /dev/null
+++ b/connector/datadogconnector/package_test.go
@@ -0,0 +1,25 @@
+// Copyright The OpenTelemetry Authors
+// SPDX-License-Identifier: Apache-2.0
+
+package datadogconnector
+
+import (
+	"testing"
+
+	"go.uber.org/goleak"
+)
+
+// The Ignore function calls prevent catching leaks generated by indirect dependencies.
+// All of these are leaks that we can't fix from within the collector code base.
+// Regarding the OpenCensus ignore: see https://github.com/census-instrumentation/opencensus-go/issues/1191
+// Regarding the DataDog ignore: see https://github.com/DataDog/datadog-agent/issues/22030
+// Regarding the cihub/seelog ignore: see https://github.com/cihub/seelog/issues/182
+func TestMain(m *testing.M) {
+	goleak.VerifyTestMain(m,
+		goleak.IgnoreTopFunction("go.opencensus.io/stats/view.(*worker).start"),
+		goleak.IgnoreTopFunction("github.com/DataDog/datadog-agent/pkg/trace/metrics/timing.(*Set).Autoreport.func1"),
+		// Unfortunately this ignore can't be anymore specific, even though it's caused by the SAP/go-hdb/driver
+		// package. There's no reference to this package in the goleak output. This has the potential of
+		// hiding future leaks, so we should remove as soon as the referenced issue is resolved.
+		goleak.IgnoreAnyFunction("github.com/cihub/seelog.(*asyncLoopLogger).processQueue"))
+}
diff --git a/internal/datadog/agent.go b/internal/datadog/agent.go
index 6399081a60d9..6dc7910ae3a0 100644
--- a/internal/datadog/agent.go
+++ b/internal/datadog/agent.go
@@ -114,6 +114,8 @@ func (p *TraceAgent) Stop() {
 		p.ErrorsSampler,
 		p.NoPrioritySampler,
 		p.EventProcessor,
+		p.TraceWriter,
+		p.StatsWriter,
 	} {
 		stopper.Stop()
 	}