Young was born in Queens, New York, the son of Josephine and Michael, a high school shop Teacher. He is of Italian descent. He was trained by Lee Strasberg at the Actors Studio. Young is a widower and has one daughter, Anne Morea. He lives in Port Washington, New York. Young served a tour of duty in the United States Marine Corps from 1957 to 1959. While in the Marine Corps, he won 32 of 34 boxing bouts. He later turned pro and compiled a 17-0 record under three different aliases. His manager was Cus D'Amato.
Young made his name playing rough-edged working class Italian-American characters, the best-known Example being his signature role as Rocky Balboa's friend (and Future brother-in-law) Paulie in Rocky (1976), for which he received an Oscar nomination for Best Supporting Actor. He is one of four actors (the other three being Sylvester Stallone, Stu Nahan and Tony Burton) who have appeared in all of the first six Rocky films (although Talia Shire, who appears in the first five films, makes a flashback appearance in the sixth). Young did not reprise his role in the 2015 film Creed, with the character described as having died in 2012.
Young participated in the 1984 New York City Marathon.
In 2017, Burt Young returned to the stage as an aged mob boss in The Last Vig, a play written by Dave Varriale. The show ran from January 14 to February 19, 2017, at The Zephyr Theatre in Los Angeles.
