Gregg was born in Boston, Massachusetts to an Episcopalian priest father, Bob Gregg. He grew up in Chapel Hill, North Carolina. He has been featured in a number of supporting roles in films, such as Lovely & Amazing, In Good Company, and The Human Stain, and a number of guest spots on TV series, such as Will & Grace, Sports Night, Sex and the City and The West Wing. He also wrote the screenplay for the 2000 thriller What Lies Beneath.

Gregg has been married since July 2001 to Jennifer Grey. The couple have one child, daughter Stella, born December 3, 2001. He co-starred with Grey in the Lifetime TV movie Road to Christmas.

Gregg attended Ohio Wesleyan University as an undergraduate and went on to get a BFA from New York University, Tisch School of the Arts, where he finished in the class of 1986.

He is the director and screenwriter of the 2008 film Choke, based on the Chuck Palahniuk novel of the same name, starring Sam Rockwell.

In 2008, Gregg appeared in the 2008 film Iron Man as S.H.I.E.L.D. agent Phil Coulson. In 2010, Gregg reprised his role as Agent Coulson for Iron Man 2. Gregg had since signed up for a multiple film deal as the character with Marvel Studios. In 2011, he shall return again as Coulson for Thor. Gregg noted his being a part of the expanding Marvel Cinematic Universe as being very exciting, "Agent Coulson was one of the guys who wasn't really in the comic books, and he was a very kind of small role in 'Iron Man," he said, "and I was just very lucky that they chose to expand that character and chosen to put him more into the universe of it. It's really a blast!" Following on from his appearance in Thor, he will again reprise his role in The Avengers.