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.
Basic of a Resignation Letter. There's no need to sugarcoat or get creative in the beginning; just state the position you're resigning from and the effective date. While you probably shared with your boss your reasons for leaving, you don't need to describe them here__keeping it simple is perfectly fine.