Friends and family packed into Perth crematorium for the service.
Rangers manager Ally McCoist and Ibrox legend John Greig were among those at the service for Redford, who was born in Perth.
Representatives from various teams he played for, including Errol Rovers - the side he started his career with - were among the mourners.
The 53-year-old was found dead in a wooded area in Irvine, North Ayrshire, on January 10. There were no suspicious circumstances.
Redford signed for Rangers in 1980 from Dundee for a then Scottish record fee of £210,000.
He spent six years at Ibrox, winning four domestic trophies, before moving to Dundee United.
He later went on to play for Ipswich Town, St Johnstone and Brechin.
After his death, many figures from Scottish football paid tribute. Tommy McLean, a former Rangers team-mate, said he was a "really lovely lad" while John MacDonald, who played with Redford at Rangers in the 1980s, said: "You couldn't meet a nicer guy off the park."
He added: "He was great to play with, I remember him scoring the winner in the 1981 League Cup final against Dundee United and that was a great day."
In a statement, Dundee United said: "The memory of his performances for United at a time when the club competed in the higher echelons of European football will forever be part of our history."