Arndt was born in McLean, Virginia. Arndt's father was a member of the Foreign Service, and as a result he lived in various countries, including Sri Lanka and India; he also lived in Virginia for a time. Arndt graduated from Langley High School in McLean, and also attended The Potomac School. He graduated from the Tisch School of the Arts at New York University. Arndt was a script reader for some time, and was a personal assistant to actor Matthew Broderick until late 1999, when he chose to begin writing screenplays full-time. His identical twin brother, David, is a professor at St. Mary's College of California.
Arndt wrote the first draft of Little Miss Sunshine in three days between May 23–26, 2000. From that initial draft, he made approximately 100 revisions over the course of a year, requesting input from friends and family. Arndt considered directing the film himself "as a no-budget, DV feature" due to his concern of the story being "just too small and "indie" to get any real attention from Hollywood". After the Endeavor Talent Agency read the script in July 2001, however, producers Albert Berger and Ron Yerxa subsequently gave the script to commercial and music video Directors Jonathan Dayton and Valerie Faris, who were immediately attracted to the project. Dayton and Faris were signed on by Producer Marc Turtletaub, who purchased the script from Arndt for $250,000, on December 21, 2001.
Arndt began collaborating with Lee Unkrich and other Pixar personnel on the screenplay for Toy Story 3 in 2006, working from a treatment by Andrew Stanton, who co-wrote the two preceding films in the series. He was nominated for Best Adapted Screenplay for his work for Toy Story 3, and became the first ever Screenwriter to be nominated for both Academy Awards for Best Original Screenplay and Best Adapted Screenplay for his first two screenplays.
In November 2012, Arndt was announced as the Screenwriter for Star Wars: The Force Awakens. In October 2013, it was announced that Lawrence Kasdan and Director J. J. Abrams were rewriting Arndt's script.
