Vaughan scored against Crystal Palace last year when only 16 years old, beating Wayne Rooney's previous record, also set whilst playing for Everton.
"I am obviously delighted that everything has been completed," he said after signing a three-year deal. "Playing professional football is what you aim for when you're growing up and now I've been given a chance to do it. It is only a chance and I know I have a lot to learn."
Vaughan has been included in Everton's Champion's League squad which leaves for Spain today.