Goulet won a 1968 Tony Award for Best Actor in a Musical for his performance in The Happy Time. He has also appeared on the Great White Way in Camelot and Moon Over Buffalo. His other theatrical credits include Little Women, Sunshine Town, Thunder Rock, The Optimist, Dreamgirls, Carousel, Finian's Rainbow, Gentlemen Prefer Blondes, The Pajama Game, Beggars Opera, Bells Are Ringing, Meet Me in St. Louis, I Do, I Do, On A Clear Day, Kiss Me Kate, The Fantasticks, South Pacific and Man of La Mancha.
In the mid-1950,s Goulet was known as Trapper Pierre in the Howdy Doody series. He began a recording career in the early 1960s. He had a hit with "What Kind of Fool Am I?" and won a Grammy Award for Best New Artist in 1963. His film credits include the animated feature film Gay Purr-ee, I'd Rather Be Rich, I Deal In Danger, Underground, Atlantic City, Beetlejuice, Scrooged, Naked Gun 2½, Mr. Wrong, Recess, The Last Producer and G-Men From Hell. He starred in the television series Blue Light, has guest-starred on numerous TV shows and headlined a number of variety specials.
La Cage aux Folles will also stars Gary Beach as Albin and Gavin Creel as Jean-Michel, Angela Gaylor as Anne, Ruth Williamson as Jacqueline, Michael Mulheren as Edouard Dindon, Linda Balgord as Mme. Dindon and Michael Benjamin Washington as Jacob.