The 18-year-old has signed a long term contract which will keep him at the club until the summer of 2023.
The agreement has been confirmed on the club’s official website.
Middleton has impressed during his cameos this season and he will be hoping to nail down a regular starting berth now.
The 18-year-old is very highly rated at the club and the Scottish youth international is expected to develop into a key first team player in future.
Middleton joined Rangers earlier this year from Norwich and he has done well to secure some game time with the first team.