Cobb was born in 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 Shakespeare productions in the New York area before breaking into television in the mid 1990s.

His first major role was on the daytime soap opera All My Children from 1994 to 1996. In 1996, Cobb was named on People magazine's annual "50 most beautiful people" list. Cobb is best known for his role as the ruthless Tyr Anasazi in the science-fiction series Andromeda from 2000 to 2002. He left the series after its third season, citing dissatisfaction over the development of his character. Upon leaving Andromeda, he joined the cast of The Young and the Restless in the role of Damon Porter.