"It is with a heavy heart and a deep sense of grief that we share the passing of our brother, husband, father and grandfather who died peacefully in Nashville surrounded by his family," his family said in a statement, according to the NY Daily News.
Thompson balanced both politics and acting throughout much of his adult life. Though he was best known for his role as District Attorney Arthur Branch on Law & Order, his other TV and film credits include Sinister, Die Hard 2, The Hunt for Red October and Cape Fear.
The Tennessee-born politician served as a conservative Republican for nine years in the U.S. Senate before retiring from his seat in 2002 when his term expired. For a brief time, he was also a GOP nominee. In 2007, he announced a bid for presidency, before shortly backing out a year later.