The following season he was sold to Celtic for £350,000, where he made just 42 appearances and grabbed 5 goals.
Falconer's clubs included Aberdeen, Watford, Middlesbrough, Sheffield United, Celtic, Motherwell, Dundee, Clydebank, St Johnstone, Grimsby Town, and finally Clyde. His playing career started in 1982 and he hung his boots up in 2003.
He could play in virtually any position on the pitch, but was most commonly used as a striker and gained a reputation as a no-nonsense, tough tackling midfielder, and was sent off the field on more than one occasion.
In 2008, Falconer became coach of a Motherwell U19 side, before moving onto Aberdeen. He now coaches youngsters at Partick Thistle. He also co-owns a property rental business in Glasgow and Aberdeen.