The best solution would be to start the docker daemon (dockerd) with a correct data root path. According to the official documentation, as of Feb 2019, there are no --graph, -g options. These were renamed to the single argument --data-root.
https://docs.docker.com/engine/reference/commandline/dockerd/
So you should modify your /lib/systemd/system/docker.service so that the ExecStart takes into consideration that argument
An example could be
ExecStart=/usr/bin/dockerd --data-root /mnt/data/docker -H fd://
Then you should restart your docker daemon. (Keep in mind that you will no longer have your containers and your images, copy the data from your old folder to the new one if you want to maintain everything)
service docker restart
Keep in mind that if you restart the docker daemon your containers will be stopped, and only those with a correct restart policy will be restarted.
Tested on Ubuntu 16.04.5 Docker version 18.09.1, build 4c52b90
