Peck's parents divorced when he was nine years old, and he and his sister were raised by their mother in the Queens neighborhood of New York City. Peck attended P.S. 217, J.H.S. 185, and LaGuardia High School of Music & Art and Performing Arts. He studied acting at the Tisch School of the Arts at New York University.
Peck's first major acting role was as the lead character in the Nickelodeon series Drake & Josh. The show ran for four seasons from 2004 to 2007 and was a critical and commercial success. Peck's other notable credits include the films Mean Creek (2004), Ice Age: The Meltdown (2006), Drillbit Taylor (2008), and The Wackness (2008).
In 2016, Peck starred in the YouTube Red original series Red vs. Blue. He also had a recurring role in the Fox comedy series Grandfathered.
In addition to his acting career, Peck is also a successful social media influencer. He has over 10 million followers on YouTube and Instagram, and he frequently posts videos about his personal life, his career, and his interests.
Peck married Paige O'Brien in June 2017. They have one son together, Max Milo Peck, who was born in December 2018.