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.
Do You Really Need to Write a Resignation Letter? Why Write a Resignation Letter? Do you really need to write a formal resignation letter? The short answer is that most of the time, no letter of resignation is necessary. Many people do believe that as an employee you need to formally resign from a job by writing a formal resignation letter to your current employer.