Garber began acting at the age of nine, joining the University of Toronto's Hart House at age 15. In 1967 he formed a folk band called The Sugar Shoppe with Peter Mann, Laurie Hood and Lee Harris. The group enjoyed moderate success, even performing on The Ed Sullivan Show and The Tonight Show Starring Johnny Carson before breaking up. He has worked in various American and Canadian movies and television, including James Cameron's Titanic (1997), in which he played the shipbuilder Thomas Andrews, and CTV's E.N.G. (1991–1993), on which he had a recurring guest role.

Other well-known appearances include Godspell (1973) as Jesus, Sleepless in Seattle (1993), Legally Blonde (2001), Annie (1999), and Tuck Everlasting (2002). In the late 1980s, he received an Emmy nomination for his portrayal of Liberace in the made-for-TV movie, Liberace: Behind the Music.

He is most well known for his portrayal of Jack Bristow on ABC's show, Alias, for which he earned three Emmy nominations.