The 20-year-old right-back has joined the Merseyside club on a five-and-a-half-year deal until the end of June 2027 and follows the arrival of Ukraine left-back Vitalii Mykolenko on New Year’s Day.
The transfer fee is believed to be in the region of £12m rising to £16m with add-ons after Rangers confirmed the deal will break the club's record sale, previously held by Alan Hutton's £9m move to Tottenham in 2008.
Everton failed in a move for Patterson during the summer window and the Scotland international expressed joy that the move to Goodison Park has now been completed.
“I’m over the moon to sign for Everton and looking forward to getting started,” Patterson told evertontv.
“It was an easy choice to sign. This is a massive club with huge history and the fanbase is tremendous. Obviously we aren’t in the place where we want to be right now but we can definitely get there with the talent in the changing room and staff here, and I have full belief we can do that.
“It is really exciting to come to a club that has huge talent in the team. I am going to work my socks off and hopefully I can do well with them in training and in games.
“It was also great for me knowing the manager really wanted me here and that made my decision. When a club really wants you, it makes your mind up early on.
“I wanted to come here from the very start. I’m delighted to be here and really looking forward to playing in front of the fans at Goodison.
“Long-term, I want to nail down a starting position and win some trophies to make the fans proud."
Patterson will wear the number three shirt at Everton and will link up with Champions League winning manager Rafa Benitez as well as the club's long-serving right-back and captain Seamus Coleman.
“I’m really looking forward to working under the manager and with my teammates," Patterson added. "I have met most of them already and everyone has made me feel so welcome.
“I’ve had a good conversation with Seamus. I am really looking forward to learning from him and working together.
“That is why I am here: to learn and get better as a player and, hopefully, win things and do well for the club. If I am working alongside Seamus that is definitely going to happen.”