You can change Docker’s storage base directory (where container and images go) using the -g option when starting the Docker daemon.
Ubuntu/Debian: edit your /etc/default/docker file with the -g option: DOCKER_OPTS="-g /path/to/new/storage"
Rhel/Fedora/Centos: edit /etc/sysconfig/docker, and add the -g option: OPTIONS='-g /path/to/new/storage'.
After a restart, (sytemctl restart docker) Docker should use the new directory.