Corddry was born and raised in Weymouth, Massachusetts, the son of Robin and Steven Corddry, who was a Massachusetts Port Authority official. He is the older brother of actor Nate Corddry. Corddry and his brother are both Eagle Scouts from Troop 19, located in Weymouth. After graduating from Weymouth North High School in 1989, Corddry went to the University of Massachusetts Amherst. According to an interview in the UMass Amherst alumni magazine, Corddry planned to study journalism when he arrived in fall 1989. He stuck with the major for just two days. English became his official major instead, but by his sophomore year, he focused much of his attention on drama classes and plays including Torch Song Trilogy, Ten Little Indians, Cat on a Hot Tin Roof, Romeo and Juliet, and Reckless. While at UMass, Corddry pledged Theta Chapter of Theta Chi fraternity. He graduated in 1993.
Corddry moved to New York City in January 1994. His early paying jobs included working as a security guard at The Metropolitan Museum of Art and handing out menus for a Mexican restaurant. He eventually landed acting jobs, including a year-long tour with the National Shakespeare Company. He trained in improv at the Upright Citizens Brigade Theatre in New York City, performing regularly as a member of the sketch comedy group -The Naked Babies- (with John Ross Bowie, Brian Huskey and Seth Morris) and spent two years with the sketch comedy group Third Rail Comedy. Corddry's first notable television appearances were on Upright Citizens Brigade on Comedy Central from 1998–2000.