Redford began his career at Dundee, and he became Scotland's most expensive footballer when he joined Rangers in 1980 for a then-record fee of £210,000.
He also played for Dundee United, Ipswich, St Johnstone, Brechin and Raith Rovers in 20-year career.
Police confirmed that Redford was found dead in Irvine, Ayrshire, and that they were not treating his death as suspicious.
A police spokeswoman said: "Around 11.15am police received a report of a man's body being found within a wooded area near to Long Drive in Irvine.
"Officers attended and enquiries are continuing. A post mortem examination will be carried out in due course to establish the exact cause of death."
A statement on the Dundee website described him as "one of the most talented kids to come through the Dens' youth system over the last few decades".
It read: "Ian was mainly a striker during his time at Dens - and he scored four goals in one match against St Mirren in 1978 in a 4-1 win, something not done by an individual since.
"It was the kind of performance that brought attention from richer clubs and Ian was sold to Rangers for a Scottish record transfer fee not long afterwards.
"While there he won trophies and his return to the city to play for rivals Dundee United saw him earn runners-up medals in the UEFA and Scottish Cups.
"Ian was a silky and attacking player who was not quite the stereotypical footballer - he'll be missed. Our thoughts are with his family and friends at this sad time."
A statement on the Dundee United website added: "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.
"His winning goal against Borussia Monchengladbach in the semi final of the UEFA Cup in 1987 will always be looked back on with particular fondness by Arabs everywhere.
"Our thoughts and prayers are with Ian's family at this very sad time."
Redford made over 170 appearances for Rangers before joining Dundee United in 1985, featuring in their UEFA Cup final defeat to IFK Gothenburg in 1987.
He joined Ipswich the following year and spent three seasons at Portman Road before returning to his homeland with St Johnstone. Redford went on to become player-manager for Brechin and finished his career with Raith Rovers in 1995.
John MacDonald, who played with Redford at Rangers in the 1980s, said: "It's unbelievable, I met him not long ago at Colin McAdam's funeral and he was in good spirits and talking away to all the boys.
"It seems the only chance you get to see former team-mates is at these sort of things or Rangers functions now.
"He was a brilliant player, his pace and skill down the wing was great and he set up a few goals for me. 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.
"You couldn't meet a nicer guy off the park. I met him at a few Rangers golf days over the years and he was great, even though we'd all slowed down a bit because we were all older.
"He was from Perthshire and although he moved when he played with Rangers, he moved back to be nearer his family after, but he always made an effort to make all the functions. It's terrible to hear, really unbelievable."
Rangers manager Ally McCoist said: "We are deeply shocked to hear the very sad news that Ian has passed away.
"I had the honour of playing with him early in my Rangers career and he was a terrific lad and an extremely talented footballer who will be sadly missed.
"Everyone at Rangers sends their sincere condolences to Ian's family and our thoughts are with them at this very difficult time."