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.
Spot the Signs. Do you have a good relationship with your manager? Is he or she relatively reasonable? Do you have regular one_on_ones where you talk about your career goals and growth? If so, it's likely that your boss will accept your resignation with grace, help develop a plan of action for your last two weeks, and maybe even attend your farewell happy hour.