I have written an Ansible role to configure Docker running on remote hosts to require verification with TLS to connect to the Docker daemon.

The role creates all the required certificates and keys, copies them to the appropriate place on each specified remote host and installs those components required by the connecting client (the machine running the Ansible code).

I did this in response to a need to secure Docker on machines on which I was using Ansible to configure a cluster of hosts forming a MongoDB replica set.

Visit the role here.