Paul was born in Missouri, but raised in Connecticut. He attended Music Theatre of Connecticut School of Performing Arts, Coleytown Middle School, and Staples High School, both in Westport, Connecticut. He graduated from the University of Michigan in December 2006 with a BFA in Musical Theatre.

He is the co-creator, with Benj Pasek of the song cycle Edges. Also with Pasek, he is one of the songwriters for the Disney Channel show Johnny and the Sprites. Pasek and Paul won the Jonathan Larson Award in 2007. He also co-wrote and co-composed the musical Dogfight, which opened Off-Broadway at the Second Stage Theatre in July 2012. He also composed the musical James and the Giant Peach with Benj Pasek.

Most recently, they have created and written the score for the stage musical Dear Evan Hansen which premiered at the Arena Stage in Washington, D.C. in July 2015. The musical, which has been called "striking for its moral complexity as well as its musical ambition", which opened on Broadway in December 2016. At the 71st Tony Awards, it is nominated for nine awards including Best Musical, Best Score, Best Book of a Musical, and Best Actor in a Musical for Platt.

Paul is married. He and his wife have an infant daughter, born in 2016.