How to set dependencies between DAGs in Airflow?

You can achieve this behavior using an operator called ExternalTaskSensor. Your task (B1) in DAG(B) will be scheduled and wait for a success on task (A2) in DAG(A)

External Task Sensor documentation

It looks like a TriggerDagRunOperator can be used as well, and you can use a python callable to add some logic. As explained here : https://www.linkedin.com/pulse/airflow-lesson-1-triggerdagrunoperator-siddharth-anand

When cross-DAG dependency is needed, there are often two requirements:

1. Task B1 on DAG B needs to run after task A1 on DAG A is done. This can be achieved using ExternalTaskSensor as others have mentioned:

   B1 = ExternalTaskSensor(task_id="B1",
                           external_dag_id='A',
                           external_task_id='A1',
                           mode="reschedule")
   

2. When user clears task A1 on DAG A, we want Airflow to clear task B1 on DAG B to let it re-run. This can be achieved using ExternalTaskMarker (since Airflow v1.10.8).

   A1 = ExternalTaskMarker(task_id="A1", 
                           external_dag_id="B",
                           external_task_id="B1")
   

Please see the doc about cross-DAG dependencies for more details: https://airflow.apache.org/docs/stable/howto/operator/external.html