David Weir, former captain of the Glasgow club, has been appointed as Warburton's assistant, a role he also filled at Brentford.
"It's a tremendous privilege and honour to manage a club of this history and tradition," Warburton told Rangers TV.
The 52-year-old takes over from Stuart McCall who was unable to lead the club back into the top flight last season.
Rangers, who were placed in administration in 2012 and forced to re-enter the lowest professional league in Scotland, were thrashed 6-1 on aggregate by Motherwell in the Championship (second tier) promotion playoff final last month.
The Glasgow club had previously won promotion in two consecutive seasons.
Warburton spent the last two seasons at London club Brentford, taking them from League One to the Championship in his first campaign and to fifth place and the playoffs in his second.
He left the club after they lost to Middlesbrough in the semi-finals of the playoffs.
(Writing by Tony Jimenez, editing by Ed Osmond)
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