He is best known for his roles as a series regular for three seasons as Gabe Lewis on the NBC sitcom The Office, as Jared Dunn on the HBO comedy series Silicon Valley, as Zach Harper on the USA Network sitcom Playing House, and as Matt Spencer on the HBO comedy show Avenue 5.

[4] His father, Jonathan, is a psychiatrist who specializes in clinical therapy, and his mother, Lisa, is a nurse practitioner.

He graduated with a Bachelor of Arts (BA) from the Gallatin School of Individualized Study at New York University.

[7][8] Woods started performing improv at the Upright Citizens Brigade Theatre at age 16 and was a part of the improvisational sketch troupe "The Stepfathers", whose members included Bobby Moynihan and Chris Gethard.

Beginning in January 2020, he had a role as Matt Spencer, Head of Customer Relations for Avenue 5, a science-fiction comedy TV series created by Armando Iannucci that premiered on HBO in the United States.