He won three major domestic trophies with the club, the Scottish League Cup in 1979 and 1980 and the Premier Division title in 1983.
In 1987, after appearing in the Uefa Cup Final, he left United for Dunfermline before finishing his playing days with Dundee.
In January 1997, Kirkwood was appointed by Instant-Dict FC, a Hong Kong First Division football team as a manager.
Kirkwood had a short caretaker manager role with St Johnstone in 2001, after Sandy Clark was sacked.
He has also held the assistant manager position at Dundee, Dunfermline and St Johnstone, and coaching roles with Livingston and Rangers.