The 21-year-old full-back has been out of action since suffering the injury in the Ibrox club's match with Annan on January 2.
Cole, who had just forced his way back into manager Ally McCoist's plans, has seen his progress stunted by a series of injury problems suffered since making his senior debut in a Champions League clash with Bursaspor in December 2010.
But boss McCoist is hopeful that the youngster's woes will be behind him after successfully going under the knife.
He told RangersTV: "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."
McCoist, meanwhile, admits he feels for striker Kevin Kyle, who has not played since injuring an ankle in a clash with Montrose goalkeeper Sandy Wood during December's 4-2 win at Links Park.
And the Light Blues boss also revealed that Chris Hegarty should be fit for Saturday's Scottish Cup tie at Dundee United after shaking off a thigh knock.