Curran died at his home in Los Angeles on Tuesday (25Oct16) after a long illness and the animated show's executive producer and showrunner Al Jean issued a statement to The Hollywood Reporter calling him "a sweet, brilliant man who said many hilarious things, some unprintable, others which will live forever in a children's cartoon.”
He also tweeted: "V v (sic) sad at the passing of Kevin Curran brilliantly funny and true friend."
Curran, who met Jean at Harvard University, began working on The Simpsons in 1998 as a consulting producer and remained with the show, writing several episodes, until 2015 - sharing three Emmys for outstanding animated program in 2003, 2006 and 2008.
He received more than 20 Emmys nominations throughout his career, and won three more in the 1980s when he served as a writer on U.S. talk show Late Night with David Letterman.
Curran also worked as writer and producer on TV shows Married... With Children, Unhappily Ever After, and The Good Life.
He is survived by his children Dashiell and Romy from his previous relationship with Bridget Jones's Diary author Helen Fielding.