Strachan, who will be 38 in February, began his career at Dundee in 1971. He moved to Aberdeen, where he won the European Cup-Winners' Cup under Alex Ferguson's management, before going to Manchester United in 1984.
Strachan, capped 50 times by Scotland, is currently recovering from his second back operation in two years but said the injury had played no part in his decision.
'I made my decision before the start of the season, and told Howard Wilkinson that this would definitely be my last season as a player. That was even before I got my back injury again,' he said.
Strachan, who already helps out coaching young players at Elland Road, seems certain to be offered a full-time coaching post.
The midfielder cost Leeds pounds 300,000 from Manchester United in March 1989, and helped the club win the Second Division title in 1990 and the First Division title two years later - Leeds' first major trophy since 1974.
'All good things come to an end. This is a big club which needs big personalities like Gordon,' Wilkinson said. 'His influence on the success we have enjoyed since those Second Division days cannot be underestimated.'
Lou Macari, the new Stoke manager, has begun a court action against Celtic, claiming more than pounds 400,000 in compensation for wrongful dismissal.
Northampton ended 97 years at the County Ground by losing 1-0 to Mansfield last night - their first defeat in six matches. The Cobblers, who will move to Sixfields, a new pounds 5.2m all-seater stadium in time for Saturday's Third Division game with Barnet, lost out to Steve Wilkinson's seventh goal of the season.