I am assuming that you are keeping your old tank running at the same time? If so you can mix some of you existing media with the new media in your new filter it will speed the process up no end, as you will be introducing the bacteria. This will quickly spread to colonize your new media. You can then replace the media from your existing tank with new media, and the same will happen in your old filter. I would recommend that you don't remove more than 30% of your old media from you existing filter though.
If however this is a replacement tank then use all the media.
Move the media, then add a little ammonia(2-3ppm).