The 20-year-old, who has won six caps for the Scotland national team, has signed a contract at Goodison Park until the summer of 2027.
Patterson is Everton’s second signing of the winter transfer window following the arrival of Ukraine left-back Vitaliy Mykolenko from Dynamo Kiev.
Patterson made seven appearances in the Scottish top flight last season as Rangers won the title, and has appeared 11 times in all competitions this term.
"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."
