Whigham was born in Tallahassee, Florida, the son of attorney Frank and school librarian Beth. The family moved to Lake Mary, Florida when Wigham was five years old. He attended Tyler Junior College in Tyler, Texas, and then transferred to the State University of New York at Purchase, New York, where he was part of a small acting program with only 31 students and a graduating class of eight seniors. After graduating, he co-founded New York City theatre troupe The Rorschach Group with his college roommate Kirk Acevedo, and served as an actor and artistic director with the troupe for three years.
Whigham appeared in one 1997 episode of the television series Ghost Stories before he received a starring role in the 2000 film Tigerland. He went on to appear in the television films Submerged, R.U.S./H., and Paradise before acting in the 2003 film All the Real Girls. Between 2004 and 2006, he appeared in the Japanese film Out of This World, the drama television series Investigation, and the films Water, Man of the House, Faith of My Fathers, Lords of Dogtown, Psychic Driving, and South of Heaven.
Whigham appeared in Pride and Glory and co-starred in the horror film Splinter, the thriller Creek, and the science fiction film Radio Free Albemuth. He had a regular role on the HBO series Boardwalk Empire as Elias "Eli" Thompson, sheriff of Atlantic City, New Jersey. In 2014, he appeared in the HBO series True Detective as disillusioned former minister Joel Theriot.