Police said a body was found in a wooded area in Irvine, North Ayrshire, on Friday.
It is understood there are no suspicious circumstances.
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."
Born in Perth on April 5, 1960, Ian Petrie Redford began his career with Dundee before joining Rangers in 1980 for a Scottish record fee of £210,000.
After six seasons with Rangers, making almost 250 appearances, he moved to Dundee United in 1985.
There he collected runners-up medals in the UEFA Cup and Scottish Cup in 1987.
Redford moved on after three years to Ipswich Town, before returning to Scotland with St Johnstone.