Jackson was born in Baton Rouge, Louisiana, and raised in Fort 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, Jackson taught social studies at LBJ High School in Austin, Texas.

Jackson 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, Jackson 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, Jackson took on the role of Rear Admiral A.J. Chegwidden (the Judge Advocate General of the Navy) in JAG, which he would continue to play for nine consecutive years. Jackson was Johnny B./Eli Ferguson in The Spitfire Grill. His mother was played by Ellen Burstyn.

Jackson returned to the role of retired admiral A.J. Chegwidden, now a civilian lawyer, in the NCIS season 10 finale, broadcast on May 14, 2013 and once again as a recurring character on NCIS: Los Angeles in its 8th and 9th seasons.