Born in Paisley, Scotland, Conti is mostly known for his stage work. He won the Tony Award in 1979 for Whose Life is it Anyway. But he is also an accomplished film and television actor. Besides taking the leading role in the 1978 TV version of Alan Ayckbourn's Norman Conquests, he played opposite Nigel Hawthorne in a long-running series of car advertisements.
He has appeared in such films as Merry Christmas, Mr. Lawrence, Reuben, Reuben (nomination for the Academy Award for Best Actor), American Dreamer, Shirley Valentine and Saving Grace.
He is married to Scottish actress, Kara Wilson.