Rangers will pay a small initial fee set to rise to £80,000 depending on appearances.
Shimmin is regarded as an outstanding prospect but Arsenal agreed to let him go after QPR tabled an offer. He also attracted interest from Charlton.
Meanwhile, Rangers have rejected an approach from Swindon for Adam Miller.
Robins boss Andy King wanted to sign the midfielder on loan but Miller is very much part of Ian Holloway's plans for this season.