Born Thomas Conti to an Italian father and an Irish Catholic mother in Paisley, Renfrewshire, he was educated at Hamilton Park School, an independent fee-paying Catholic boys' school in Glasgow, and at the Royal Scottish Academy of Music and Drama.

Conti began working with the Dundee Repertory in 1959. He appeared on Broadway in Whose Life is it Anyway? in 1979. In London he played the lead in Jeffrey Bernard is Unwell at the Garrick Theatre.

Conti also is an accomplished film and television actor. Besides taking the leading role in the 1978 TV version of Alan Ayckbourn's Norman Conquests, he appeared in the Princess and the Pea episode of the family television series Faerie Tale Theatre, guested on Friends and Cosby, and played opposite Nigel Hawthorne in a long-running series of car advertisements in the UK.

Conti has appeared in such films as Merry Christmas, Mr. Lawrence, Reuben, Reuben, American Dreamer, Shirley Valentine, Saving Grace and Dangerous Parking.

Conti's book The Doctor, about a former Secret Operations pilot with Intelligence Services, was published in 2004.

Conti has been married to Scottish actress Kara Wilson since 1967, and their daughter Nina is an actress and ventriloquist.