He is best known for his roles as the ruthless Nietzschean mercenary Tyr Anasazi in the science-fiction series Gene Roddenberry's Andromeda from 2000 to 2002 and as Noah Keefer on All My Children from 1994 to 1996.
Cobb was born in North Tarrytown, New York; he graduated from New York University's Tisch School of the Arts in 1987. A classically trained actor, he appeared in a number of Shakespearean productions in the New York area before breaking into television in the mid-1990s. One of his first movies was the 1995 film Eyes Beyond Seeing in which he plays a mental patient who claims to be Jesus Christ.
In 1999, Cobb was in two episodes of the Beastmaster television series, portraying a character very similar to his character from Andromeda.
In 1996, Cobb was named on People magazine's annual list of the "50 most beautiful people".
He left the Andromeda TV series at the start of the fourth season, citing dissatisfaction over the development of his character.