Funt achieved a BA in Fine Arts from Cornell University in 1934 and studied business administration at Columbia University. He began the show on ABC Radio in 1946 as Candid Microphone and soon experimented with a visual version by doing a series of theatrical short films also known as Candid Microphone. These film shorts served as a springboard for his entrance into television on August 10, 1948.

In the 1963—1964 season, he appeared as an albino orangutan on the episode, "Smile, Todd, You're on Candid Camera," of The New Phil Silvers Show, starring comedian Phil Silvers as factory foreman Todd Deal.

Funt wrote several books, beginning with Eavesdropper at Large: Adventures in Human Nature with "Candid Mike" (Vanguard Press, 1952). He followed Candid Kids (Bernard Geis, 1964) with Candidly, Allen Funt: A Million Smiles Later (Barricade Books, 1994).

During the 1970s, Funt made two documentary films based on the hidden camera theme: What Do You Say to a Naked Lady? (1970) and Money Talks (1972). Funt also produced a syndicated version of Candid Camera from 1974 to 1979; his co-hosts included, at various times, John Bartholomew Tucker and Jo Ann Pflug. In the 1980s, Funt produced a series of adult-oriented video called Candid Candid Camera.

He amassed a collection of works by the Victorian painter Lawrence Alma-Tadema, but was forced to sell them just before the painter's reputation revived and the prices of the paintings shot up.

Born in New York City, Funt lived for a short time in Westchester County, New York in Croton-on-Hudson. His White Gates estate was sold to opera singer Jessye Norman in the early 1990s. Following a stroke in 1993, he became incapacitated and died in Pebble Beach, California. Candid Camera continued with his son, Peter Funt, as host.