The former Brentford boss will have Davie Weir as his assistant at Ibrox – the former Rangers skipper also worked alongside Warburton at Griffin Park.
Warburton takes over from Stuart McCall, who only took charge on a short-term deal in March – replacing caretaker boss Kenny McDowall – but failed to secure promotion back to the Premiership after Rangers were beaten by Motherwell in the play-off final.
McCall had to re-apply for the job as the Rangers board weighed up their options for next season and they have now opted to appoint Warburton instead.
Warburton, assisted by former Scotland international defender Weir, guided Brentford to promotion from League One in 2013/14 before taking them into the Sky Bet Championship play-offs this year.
However, the London side announced in February that Warburton would depart at the end of the season leaving him free to take the Gers post and start rebuilding a squad that will be shorn of at least 10 players.
Warburton, 52, said earlier this month: “From my point of view they are a massive club. I have huge respect for the size of the club and the fan base at Rangers. Who wouldn’t?
“I am well aware of the tradition and history of the club so I would never be anything other than absolutely respectful of a club of that stature.”
Warburton will become just the 15th man to have held the position of manager in Rangers’ 143-year history.