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.
Otherwise, look to the history of your company. How have your boss and other managers handled employees' resignations? If you see a pattern of upper management refusing to let the team members work out their notice, you can likely expect the same.