Remember that when you drag from the internal drive to the external, it defaults to a copy process, not a move. So when you open your project, the media will still be linked to the files on your internal drive.
So in addition to Loren's suggestion, I'd also ensure the following:
1. Backup up your project file first to an external medium, in case the relink goes haywire. Wrong relinks are very hard to correct, so saving a copy of your project file (which remembers the old file locations) will be useful;
2. Move all your media to one folder on the external drive, if possible. Your relink process will be much, much faster. However, do NOT mix non-recapturable media (eg. graphics, PSDs, second-generation clips, manually captured clips) with recapturable media (ie. batchlisted clips);
3. Since you're consolidating your footage, make sure you have no repeat file names -- each and every media file must have a unique name. If you have duplicates, you must correct them first by hand, slowly, all the while comparing duplicate file names with their references in FCP to make sure they aren't different files with the same name;
4. When you're ready to dump the media on your internal drive, put it into the Trash, but don't empty yet. Launch the project file and complete the relinking process to the media on the external drive. Check the "manual" button -- if you have a lot of media and have moved most of it to one folder on the external drive, manual relinking will be much faster. Complete the relinking. If nothing's missing or gone bad, then empty the Trash. This is an insurance policy to make sure you didn't get rid of any files by mistake.