Morrow was born in New Rochelle, New York, of Jewish heritage, the son of Diane Francis (née Markowitz), a dental hygienist, and Murray Morrow, an industrial lighting manufacturer. His parents divorced when he was nine. He is married to actress Debbon Ayer, and together they have a daughter named Tu Simone Ayer Morrow.

Morrow played the lead role of Joel Fleischman in the award-winning television show Northern Exposure from 1990-1995. Afterward, he starred in the critically acclaimed film, Quiz Show, as Dick Goodwin, a Congressional investigator intent on uncovering the corruption behind the 1950s’ game show scandal, and played Albert Brooks' sports agent brother in Mother. At one point, he was slated to play the protagonist in the 1996 film version of The Island of Dr. Moreau, but he dropped out of the project and was replaced by David Thewlis. In 2000, he directed and starred in Maze about an artist with Tourette syndrome. In 2002, he played Kevin Hunter on the Showtime television series, Street Time. He also appeared in the TV movie Custody. He is currently starring next to David Krumholtz and Judd Hirsch in Numb3rs on CBS.