The centre back completed a medical last night before the signing was finalised today.
The former Tynecastle centre-back has sealed his return to the club where he started his career. He left Rangers in 2010 to sign for Liverpool for £2 million.
Rangers are also close to completing the signing of Rob Kiernan from Wigan Athletic. The defender was pictured arriving at Ibrox last night.
Warburton is also looking to sign 35-year-old former Watford and Derby midfielder John Eustace to guide what he hopes will be a predominantly youthful squad.
Warburton said: “We are making good progress and there are hopefully a positive few days ahead.
“We are looking for a young, hungry squad that want to play here but at the same time you need one or two senior mentors to look after them, not just on the pitch but off the pitch too.
“People like John Eustace are few and far between. We are having a chat and seeing how far we can take it, no more than that.”