The former Brentford boss heads to Ibrox with club legend David Weir as his assistant - after working together at Griffin Park for the last 18 months.
The 52-year-old becomes the first Englishman to manage the Scottish Championship club and follows Stuart McCall who had the role on an interim basis.
Warburton left Brentford at the end of last season having guided them into the Championship play-offs at the first time of asking.
The west London club appointed Dutchman Marinus Dijkhuizen last month as they aim to build a new structure at the top of the club.
Weir, who left Ibrox three-and-a-half years ago and captained the club to three SPL titles, departed with Warburton.
The duo's appointment at Ibrox comes after the club failed to win promotion to the top flight.
Rangers have risen through the divisions following relegation to the bottom tier, but were beaten by Motherwell in the Scottish Premiership play-off final over two legs.