Morton was born in The Bronx, a borough of New York City, New York. He is the son of Evelyn, a secretary, and Joseph Thomas Morton, Sr., a U.S. army ntelligence officer. Because of his father's profession, he spent parts of his childhood in West Germany and Okinawa. Morton graduated from Hofstra University.
Morton made his Broadway theatre debut in Hair, appeared in Salvation, and was nominated for a Tony Award for Raisin. He has appeared in over 70 movies, including Terminator 2: Judgment Day (as Dr. Miles Bennett Dyson) and Blues Brothers 2000 (as 'Cabel "Cab" Chamberlain', based upon the late Cab Calloway), and has made many notable TV guest appearances, including his appearances as Dr. Steven Hamilton in the first two seasons of Smallville.
On television, Morton has starred in the Sanford and Son spin-off series Grady (1975–1976), Equal Justice (1990–91), Under One Roof (1995), and E-Ring (2005). More recently, he portrayed the jack-of-all-trades scientist, Henry Deacon, as a regular on Sci-Fi Channel's 'Eureka (2006-2012). Morton has also directed and produced. He has made several appearances as a defense attorney on Law & Order.
On daytime TV, Morton has had roles on Search for Tomorrow (Dr. James Foster, 1973–74), Another World (Dr. Abel Marsh and Leo Mars, 1983–84), and All My Children (Dr. Zeke McMillan, 2002). In 2002, he appeared on the London stage in the play Art.
In October 1984, Morton married Nora Chavooshian, the production designer for The Brother from Another Planet. The couple has three children: daughters Hopi and Seta, and son Ara, as well as a grandson, named Moses.