diff --git a/cosmos/core/airflow.py b/cosmos/core/airflow.py
index 9e1d08ac1..ca0d3cd6f 100644
--- a/cosmos/core/airflow.py
+++ b/cosmos/core/airflow.py
@@ -1,13 +1,17 @@
 import importlib
 
+import airflow
 from airflow.models import BaseOperator
 from airflow.models.dag import DAG
 from airflow.utils.task_group import TaskGroup
+from packaging.version import Version
 
 from cosmos.core.graph.entities import Task
+from cosmos.dataset import get_dataset_alias_name
 from cosmos.log import get_logger
 
 logger = get_logger(__name__)
+AIRFLOW_VERSION = Version(airflow.__version__)
 
 
 def get_airflow_task(task: Task, dag: DAG, task_group: "TaskGroup | None" = None) -> BaseOperator:
@@ -29,6 +33,13 @@ def get_airflow_task(task: Task, dag: DAG, task_group: "TaskGroup | None" = None
     if task.owner != "":
         task_kwargs["owner"] = task.owner
 
+    if module_name == "local" and AIRFLOW_VERSION >= Version("2.10"):
+        from airflow.datasets import DatasetAlias
+
+        # ignoring the type because older versions of Airflow raise the follow error in MyPU
+        # error: Incompatible types in assignment (expression has type "list[DatasetAlias]", target has type "str")  [assignment] Found 1 error in 1 file (checked 3 source files)
+        task_kwargs["outlets"] = [DatasetAlias(name=get_dataset_alias_name(dag, task_group, task.id))]  # type: ignore
+
     airflow_task = Operator(
         task_id=task.id,
         dag=dag,
diff --git a/cosmos/dataset.py b/cosmos/dataset.py
new file mode 100644
index 000000000..3c43eb1bb
--- /dev/null
+++ b/cosmos/dataset.py
@@ -0,0 +1,30 @@
+from airflow import DAG
+from airflow.utils.task_group import TaskGroup
+
+
+def get_dataset_alias_name(dag: DAG | None, task_group: TaskGroup | None, task_id: str) -> str:
+    """
+    Given the Airflow DAG, Airflow TaskGroup and the Airflow Task ID, return the name of the
+    Airflow DatasetAlias associated to that task.
+    """
+    dag_id = None
+    task_group_id = None
+
+    if task_group:
+        if task_group.dag_id is not None:
+            dag_id = task_group.dag_id
+        if task_group.group_id is not None:
+            task_group_id = task_group.group_id
+    elif dag:
+        dag_id = dag.dag_id
+
+    identifiers_list = []
+    dag_id = dag_id
+    task_group_id = task_group_id
+
+    if dag_id:
+        identifiers_list.append(dag_id)
+    if task_group_id:
+        identifiers_list.append(task_group_id.replace(".", "__"))
+
+    return "__".join(identifiers_list)
diff --git a/cosmos/operators/local.py b/cosmos/operators/local.py
index 2ba2b18ff..e95907042 100644
--- a/cosmos/operators/local.py
+++ b/cosmos/operators/local.py
@@ -9,6 +9,7 @@
 from pathlib import Path
 from typing import TYPE_CHECKING, Any, Callable, Literal, Sequence
 
+import airflow
 import jinja2
 from airflow import DAG
 from airflow.exceptions import AirflowException, AirflowSkipException
@@ -16,6 +17,7 @@
 from airflow.utils.context import Context
 from airflow.utils.session import NEW_SESSION, create_session, provide_session
 from attr import define
+from packaging.version import Version
 
 from cosmos import cache
 from cosmos.cache import (
@@ -24,6 +26,7 @@
     is_cache_package_lockfile_enabled,
 )
 from cosmos.constants import InvocationMode
+from cosmos.dataset import get_dataset_alias_name
 from cosmos.dbt.project import get_partial_parse_path, has_non_empty_dependencies_file
 from cosmos.exceptions import AirflowCompatibilityError
 from cosmos.settings import LINEAGE_NAMESPACE
@@ -42,6 +45,7 @@
     from dbt.cli.main import dbtRunner, dbtRunnerResult
     from openlineage.client.run import RunEvent
 
+
 from sqlalchemy.orm import Session
 
 from cosmos.config import ProfileConfig
@@ -72,6 +76,8 @@
     DbtTestMixin,
 )
 
+AIRFLOW_VERSION = Version(airflow.__version__)
+
 logger = get_logger(__name__)
 
 try:
@@ -387,7 +393,7 @@ def run_command(
                     outlets = self.get_datasets("outputs")
                     self.log.info("Inlets: %s", inlets)
                     self.log.info("Outlets: %s", outlets)
-                    self.register_dataset(inlets, outlets)
+                    self.register_dataset(inlets, outlets, context)
 
                 if self.partial_parse and self.cache_dir:
                     partial_parse_file = get_partial_parse_path(tmp_dir_path)
@@ -468,20 +474,26 @@ def get_datasets(self, source: Literal["inputs", "outputs"]) -> list[Dataset]:
             )
         return datasets
 
-    def register_dataset(self, new_inlets: list[Dataset], new_outlets: list[Dataset]) -> None:
+    def register_dataset(self, new_inlets: list[Dataset], new_outlets: list[Dataset], context: Context) -> None:
         """
         Register a list of datasets as outlets of the current task.
         Until Airflow 2.7, there was not a better interface to associate outlets to a task during execution.
         """
-        with create_session() as session:
-            self.outlets.extend(new_outlets)
-            self.inlets.extend(new_inlets)
-            for task in self.dag.tasks:
-                if task.task_id == self.task_id:
-                    task.outlets.extend(new_outlets)
-                    task.inlets.extend(new_inlets)
-            DAG.bulk_write_to_db([self.dag], session=session)
-            session.commit()
+        if AIRFLOW_VERSION < Version("2.10"):
+            with create_session() as session:
+                self.outlets.extend(new_outlets)
+                self.inlets.extend(new_inlets)
+                for task in self.dag.tasks:
+                    if task.task_id == self.task_id:
+                        task.outlets.extend(new_outlets)
+                        task.inlets.extend(new_inlets)
+                DAG.bulk_write_to_db([self.dag], session=session)
+                session.commit()
+        else:
+            dataset_alias_name = get_dataset_alias_name(self.dag, self.task_group, self.task_id)
+            for outlet in new_outlets:
+                context["outlet_events"][dataset_alias_name].add(outlet)
+                # TODO: check equivalent to inlets
 
     def get_openlineage_facets_on_complete(self, task_instance: TaskInstance) -> OperatorLineage:
         """