Dye was born in New Orleans, Louisiana. Dye's family moved around the United States and in the mid-1970s he attended Sylvania High School in Sylvania, Ohio. Later, Dye moved to California and attended Mills High School in Millbrae, California and UCLA. He was married to Actress Laura San Giacomo from 1990–1998, with whom he has a son named Mason. He also has a son, Calvin, with Actress Tracy Middendorf.