Burrows was born in Los Angeles, California, the son of Ruth (Levinson) and Abe Burrows, who was a well-known composer, director and writer. Burrows is a graduate of Oberlin College. He also went to the Yale School of Drama.
Burrows' style is best known for his comic timing, complex blocking for actors, and incorporating more sophisticated lighting in television studio shoots. He is also credited for expanding the typical multi-camera television shoot from three to four cameras.
Burrows has directed for many shows, including:
- 1970s – The Mary Tyler Moore Show, The Bob Newhart Show, Rhoda, Laverne & Shirley, Taxi, The Associates
- 1980s – Cheers (which he also co-created), The Hogan Family, Dear John
- 1990s – Wings, Frasier, Friends, NewsRadio, 3rd Rock from the Sun, Pearl, Dharma & Greg, Caroline in the City, Will & Grace, George & Leo
- 2000s – The Class, Courting Alex, Two and a Half Men, Back to You, The Big Bang Theory, Gary Unmarried, Hank
- 2010s – Romantically Challenged, Mike & Molly, Better with You, $#*! My Dad Says, 2 Broke Girls, Partners
Burrows has had cameo appearances in several of the shows for which he has directed. He also appears as a television director in the 2005 HBO series The Comeback. Burrows played himself on the series. Burrows has been nominated for fifteen Directors Guild of America awards, and for an Emmy Award every year between 1980 and 2005, excluding 1997.
An episode of Scrubs, "My Life in Four Cameras", had a character named "Charles James" in honor of Cheers creators Burrows and Glen and Les Charles.