The winger passed a medical earlier today and becomes Rangers' 11th signing of the summer transfer window.
Kent had been linked with a return to Scotland throughout the summer and featured for Jurgen Klopp's side in their pre-season tour of the United States.
Belgian giants Club Brugge and Championship side Leeds were also credited with an interest but Kent had his heart set on a reunion with Steven Gerrard.
The 22-year-old impressed on loan from the Anfield side last season, winning the PFA Scotland Young Player of the Year award as well as being included in the PFA's Team of the Season.
Kent scored six goals for Rangers and laid on nine for his team-mates in 43 appearances in all competitions.