Use Git to version control your config file (~/.atom/config.cson), and any other config files (dotfiles) you may have.
You can then host your Git repository for free on somewhere like GitHub, and retrieve it on other computers simply by running git clone https://github.com/{username}/{repo}.
You can then keep it up to date using git push (to upload changes) and git pull (to download changes).
To track installed packages as well, you will need to run:
apm list --installed --bare > ~/.atom/package.list
And add that file to Git also. To restore, use:
apm install --packages-file ~/.atom/package.list