The 21-year-old full-back has been out of action since suffering the injury against Annan Athletic on 2 January.
Manager Ally McCoist said: "The operation has taken place and it went well.
"Surgery is something we feared before the Annan game when he suffered the injury because we were worried his ankle was not strong enough. Sadly that has happened.
"He has required a restructuring of the ankle and the surgeon has told us he is happy with the way things have gone.
"So that's the season over for Darren but hopefully he has set his sights on being back strong in the summer with a view to next season."
Meanwhile, Rangers have revealed that midfielder Lewis MacLeod will be out of action for up to two months after a scan revealed he has damaged medial ligaments in his knee.
The teenager was carried off in the first half of Saturday's 1-1 draw with Montrose at Ibrox after a collision with Paul Dawson.