Meek graduated from Arlington High School in Riverside, California, and attended the University of California at Irvine. After graduating from UCI with a Bachelor of Arts degree in Drama in 1983, he then moved to New York City to pursue a career on Broadway.
Meek returned to California, and appeared in several film and television roles, including Mortal Kombat: Conquest, in which he played the thunder god Raiden and the supreme antagonist Shao Kahn. He also played the role of a demon on the supernatural drama, Charmed. He gained a fan following after appearing as Jonathan Raven on the CBS Television martial arts series Raven in 1992 and 1993.
From October 2006 to April 2007, Meek joined As the World Turns in the contract role of Craig Montgomery, making him the third actor to portray the role after Scott Bryce and Hunt Block.