Stack was born in Los Angeles, California but spent his early childhood growing up in Europe. He became fluent in French and Italian at an early age, but he did not learn English until returning to Los Angeles.
Stack took drama courses at the University of Southern California. His deep voice and good looks attracted producers in Hollywood. When Stack visited the set of Universal Studios at age 20, producer Joe Pasternak offered him an opportunity to enter the business. Recalled Stack, "He said 'How'd you like to be in pictures? We'll make a test with Helen Parrish, a little love scene.' Helen Parrish was a beautiful girl. 'Gee, that sounds keen,' I told him. I got the part."
In 1957, Stack was nominated for an Academy Award for Best Supporting Actor for Written on the Wind. He starred in more than 40 films, including The Iron Glove (1954); Good Morning Miss Dove (1955) and Is Paris Burning? (1966). Known for his steadfast, humorless demeanor, he made fun of his own persona in comedies such as 1941 (1979), Airplane! (1980), Caddyshack II (1988), and Baseketball (1998).
Stack depicted the crimefighting Eliot Ness in the television drama The Untouchables from 1959 to 1963. The show portrayed the ongoing battle between gangsters and federal agents in a Prohibition-era Chicago. His role on the show brought Stack a best actor Emmy Award in 1960.
He began hosting Unsolved Mysteries in 1988, where his deep, ominous voice and expressionless face lent an authentic seriousness to the show's dark subject matter.
Stack had undergone radiation therapy for prostate cancer in October 2002. He died of heart failure at his home in Los Angeles in May 2003. He is interred in the Westwood Village Memorial Park Cemetery in Westwood, California.