Born in Connecticut, he was the son of Hannah (née Clifford) and Michael Joseph Begley, Irish immigrants. His older brother was Edward James Begley, Sr. (1901-1970) an Academy Award-winning actor of theatre, radio, film, and television.
He was elected to The Lambs in 1945. After 25 years as an actor-dancer, Begley switched to the production end of the industry. From 1949-1958 he was head of the casting department of NBC-TV. For five years after this he was a talent negotiator and casting director for the large advertising agency Lennen & Newell, Inc.
His wife was Dorinda Marie Begley. She died in 1972.
He died March 6, 1985 in Broward, Florida. Martin J. Begley is interred in Cemetery of the Holy Rood, Westbury, Long Island.