The son of Mary Lee and Douglas Rapp, he was born and raised in Joliet, Illinois, with his brother, actor Anthony Rapp, and sister, Anne. His parents divorced when Rapp was five, and he and his siblings were raised by their mother, who died in 1997. He graduated from Clarke College in Dubuque, Iowa, where he played varsity basketball. He also completed a two-year playwriting fellowship at The Juilliard School.

Rapp is the author of numerous young adult novels. His first adult novel, The Year of Endless Sorrows, was released in December 2006. Rapp made his graphic novel debut with the release of Ball Peen Hammer through First Second Books in September 2009. He has another graphic novel, Decelerate Blue, in the works.

Rapp's novel The Buffalo Tree was censored by the Muhlenberg School Board in Reading, Pennsylvania due to its themes, graphic language and sexual content.

Rapp directed his first film, Winter Passing with Zooey Deschanel and Will Ferrell in 2005, and was a creative consultant for the television show The L Word.

Rapp was a member of the band Bottomside, which released the independent CD The Element Man in September 2004. He is currently a member of Less the Band, which released Bear in April 2006.