You'll obviously have to set up Ruby, Rails, your database and the
appropriate Ruby database library on your Linux machine first. And
then if you have any other external gems/libraries that your app
relies on, you'll have to install those separately on your Linux
machine as well.
Apart from that, your app should be able to move across with no
changes. There are a lot of people who work in OS X and then deploy to
Linux servers, which is basically the same thing.