Info says: "Currently, only the bind mount volume type and EFS volume type are supported". But there is no option for EFS.
I read aws article https://aws.amazon.com/premiumsupport/knowledge-center/efs-mount-on-ecs-container-or-task/ : "5. Enter the name of the volume, and then select EFS from the Volume types drop-down menu."
I created SG for EFS that allows access to port 2049 from the security group of my EC2 cluster. I created efs in the same vpc and subnets and attached SG for EFS to all mount points.
But that doesn't help. The console doesn't offer me EFS volume type.
Now that the new ECS experience is live, the updated portal also has EFS support. To achieve that, fill in the required details in Step 1 and click Next.
In step 2, under storage, click on "Add volume" and select EFS as the Volume type.
The new ECS experience (top left corner) gives a pretty bad half baked UI to the options that are available. If you disable that, and use the "old experience" and create a new task definition and scroll all the way to the bottom, there's an option to add Volumes where you can add EFS as the volume type.