Jackson was born in Baton Rouge, Louisiana, and raised in Ft Worth, Texas. He played football and basketball at Arlington Heights High School in Fort Worth, graduating in 1968. After graduating from the University of Texas at Austin, he taught social studies at LBJ High School in Austin, Texas.

He started acting in his late 20s, at a community theater. In 1980, Jackson went to New York City, and later to Hollywood, to further his acting career. He had small roles in a number of television and motion picture productions, most notably a recurring role in the series Wiseguy. In 1986, he appeared in the TV film Blind Justice, starring Tim Matheson. In 1987, he had a small role in the Macgyver episode "Birth Day" as LA police sergeant Meechum who recognises MacGyver's flag help signal, saying he does so because he spent four years in the Navy. In 1992, Jackson played Captain West, a JAG Officer, in the American drama film A Few Good Men.

In 1996, he took on the Chegwidden role in JAG, which he played for nine seasons as Rear Admiral Albert Jethro 'A.J.' Chegwidden, Judge Advocate General of the United States Navy. He was Johny B./Eli in Spitfire Grill. His mother was played by Ellen Burstyn.

He returned to the role of retired Rear Admiral A.J. Chegwidden, now a civilian Lawyer, in the NCIS season 10 finale, broadcast on May 14, 2013 and again on NCIS: Los Angeles Season 8, broadcast on February 19, 2017.