Finlay was nominated for the Turner Prize in 1985. He was awarded honorary doctorates from Aberdeen University in 1987, Heriot-Watt University in 1993 and the University of Glasgow in 2001, and an honorary and/or visiting professorship from the University of Dundee in 1999. The French Communist Party presented him with a bust of Saint-Just in 1991. He received the Scottish Horticultural Medal from the Royal Caledonian Horticultural Society in 2002, and the Scottish Arts Council Creative Scotland Award in 2003. Awarded in the Queen's New Year's Honours list in 2002, Finlay was a CBE.