Police said Mr Redford, who was just 53 and had a glittering career with Dundee, Ipswich, St Johnstone and Raith Rovers, was found in a wooded area in Irvine, North Ayrshire, on Friday.
It is understood there are no suspicious circumstances.
Tributes have been paid by former team-mates and fans of the club.
Mr Redford started his career with Dundee before joining Rangers for a then Scottish record fee of £210,000 in 1980.
The midfielder moved to Dundee United in 1985 where he played in their Uefa Cup Final defeat to IFK Gothenburg in 1987.
Both Dundee and Dundee United have paid fulsome tributes to their former player.
A statement on the club's 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."
Dundee United, who he played with between 1985 and 88, 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 and 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."
John MacDonald, who played with Redford at Rangers in the 1980s, said: "It's unbelievable, I met him not long ago at [Former Rangers player] 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."
Mid-Scotland and Fife Tory MSP Murdo Fraser tweeted: Very sad to hear of the untimely death of Ian Redford. A great servant to the club #RFC"
A Police Scotland spokeswoman said: "At around 11.15am on Friday police received a report of a man's body being found within a wooded area near to Long Drive in Irvine.
"Officers are investigating and inquiries are continuing.
"A post mortem will be carried out in due course to establish the cause of death."
Read Michael Grant's interview with Ian Redford last year here