Bright started his professional career under the tutelage of his father, Jackie Bright. Born to a Jewish-American family, Bright attended the East Side Hebrew Institute on the Lower East Side of Manhattan. After graduating magna cum laude from Emerson College, he worked in New York with Joseph Cates, where he produced specials for George Burns, Johnny Cash, David Copperfield and Dolly Parton.
After moving to Los Angeles in 1982, he started work in comedy programming such as The History of White People in America and comedy specials starring Robin Williams, Martin Mull, Harry Shearer, Paul Shaffer and Merrill Markoe.
In 1993, Bright entered a partnership with Marta Kauffman and David Crane to form Bright/Kauffman/Crane Productions and began a development deal with Warner Brothers Television to produce the comedy series Friends. He also directed 42 episodes of the series.
After "Friends", he went on to Executive Produce the spinoff series "Joey" with Friends producers Shana Goldberg-Meehan and Scott Silveri. It starred Friends actor Matt Leblanc and featured Jennifer Coolidge, also an Emerson College graduate. Joey was cancelled in May 2006 during its second season after a major ratings slump.
After Joey, Bright moved back to his college town of Boston, where he began teaching at his alma mater, Emerson College. At the school, he taught several classes in about sitcom producing and directing. He also executive produced two productions for the school's The Emerson Channel. One was a sketch comedy hour titled "Zebro: A Laugh Show", and the other a sitcom set at the school titled Browne at Midnight, written by Brad Woolf and Dan Borrelli, that followed a freshman DJ at the school's station WERS 88.9FM. Kevin Bright is married to Claudia Bright, with two kids, twins, Zachary and Justin.