How to move/rename a file using an Ansible task on a remote system

The file module doesn't copy files on the remote system. The src parameter is only used by the file module when creating a symlink to a file.

If you want to move/rename a file entirely on a remote system then your best bet is to use the command module to just invoke the appropriate command:

- name: Move foo to bar
  command: mv /path/to/foo /path/to/bar

If you want to get fancy then you could first use the stat module to check that foo actually exists:

- name: stat foo
  stat: path=/path/to/foo
  register: foo_stat

- name: Move foo to bar
  command: mv /path/to/foo /path/to/bar
  when: foo_stat.stat.exists

From version 2.0, in copy module you can use remote_src parameter.

If True it will go to the remote/target machine for the src.

- name: Copy files from foo to bar
  copy: remote_src=True src=/path/to/foo dest=/path/to/bar

If you want to move file you need to delete old file with file module

- name: Remove old files foo
  file: path=/path/to/foo state=absent

From version 2.8 copy module remote_src supports recursive copying.