You want your intent to be as direct as possible. You are leaving, plain and simple. There's no need to mention where you're going. You can discuss that with your boss (though you're not obligated to do so) and your colleagues if you want, but there's little purpose for including that in your resignation letter. That's especially true if you're moving over to a competitor__you don't want to create ill will in this letter or cause any drama.
Prepare for It. In this case, all you can do is politely deliver your resignation, then strive to make the transition as easy as possible for your team. Your manager may not have the ideal reaction to your news__and your workplace may not be the most pleasant environment for the next two weeks__but to avoid burning bridges, it's best to work through it with a positive attitude.