Dexter was born Veljko Šošo (Serbian Cyrillic: Вељко Шошо), in Goldfield, Nevada, of Serbian descent. He spoke Serbian as his first language. Burly, dark and handsome, Brad Dexter was usually given supporting roles of a rugged character. Early in his acting career, he went by the name of Barry Mitchell. After a stint as an amateur boxer, Dexter attended the Pasadena Playhouse where he studied acting. During World War II he enlisted for military service with the U.S. Army Air Corps and appeared in the Corps play and film Winged Victory. His career in Hollywood spanned over four decades. Other films Dexter appeared in include The Asphalt Jungle, Run Silent, Run Deep, Last Train from Gun Hill, Kings of the Sun, Johnny Cool, Shampoo, Vigilante Force and House Calls. From January to November 1953 he had a brief and stormy marriage with singer/composer Peggy Lee which ended in divorce. His friendship with Frank Sinatra began when Dexter saved the singer from drowning on May 10, 1964, during production of the World War II film, None but the Brave, on the island of Kauai in Hawaii. Sinatra and Ruth Koch, the wife of producer Howard Koch, were swimming at a beach when they were swept out to sea by the outgoing tide and nearly drowned. Sinatra’s co-star Dexter and two surfers swam out and rescued them. Dexter was later awarded a Red Cross medal for his bravery.

Sinatra and Dexter co-starred in a second film together Von Ryan’s Express and Dexter subsequently produced The Naked Runner which starred Sinatra and was filmed in London. The two men clashed over Sinatra’s unwillingness to finish the film and after it was completed, Dexter resigned. “I was the only guy who dropped Sinatra … I couldn’t put up with his nonsense”, Dexter said at the time. Dexter also co-produced Skag with fellow Serbian American actor Karl Malden. He appeared in many television series, including Richard Diamond, Private Detective, Colt .45, Bourbon Street Beat, and Mannix. He was married to Star-Kist tuna heiress Mary Bogdonovich from January 27, 1971 until her death on June 12, 1994. Later in 1994 he married June Deyer and remained with her until his death. He died in Rancho Mirage, California, from emphysema, on December 11, 2002, at age 85, and is interred at Desert Memorial Park