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. Your best option in this scenario is to accept it with dignity and make sure you're ready to leave the office for good when you turn in your resignation letter, whether that means gathering up your personal items or making sure you've collected the names and contact information for the teammates and clients you'd like to stay in touch with.