Henchy was born in New York City, to Patricia Henchy. He was raised in Augusta, Georgia and attended Saint Mary on the Hill Catholic School. He graduated from Friendswood High School in 1982, where he was active in journalism and was a member of the yearbook staff. He attended the University of New Mexico, where he received a B.S. degree in Finance and was a member of the Sigma Alpha Epsilon chapter.

Henchy went on to write for Campus Cops in 1996. After writing for a few television specials and some guest-writing stints on series, Henchy created and produced television series Battery Park in 2000, which starred Elizabeth Perkins.

Henchy met Actress, author and model Brooke Shields in 1999 on the Warner Bros lot. They became engaged in July 2000 while on vacation in Mexico and married on April 4, 2001. They have two daughters:

Henchy was a Writer and Producer for television sitcoms Spin City and Life With Bonnie. He created the sitcom I'm with Her with Marco Pennette, which was loosely based on Henchy's relationship with wife Brooke Shields. The show was cancelled by ABC after one season. Henchy later became the co-executive Producer of Entourage and a Producer on HBO's Eastbound & Down. He, along with Will Ferrell and Adam McKay, created the website Funny or Die. Henchy produced The Goods: Live Hard, Sell Hard. He is credited as a Writer of the 2009 film Land of the Lost, The Other Guys and The Campaign which he also co-produced. In March 2018 it was announced that Henchy will direct a feature-length movie for the Impractical Jokers television series. The film will be produced by Funny or Die. The film is set to go into production in Spring 2018.