Born Brad H. Gerstenfeld, his father was a hearing aid specialist working in geriatrics and his mother a housewife. He attended Hale Jr. High School in Woodland Hills, California and graduated from El Camino Real High School in Woodland Hills, California in 1978. He attended UCLA for less than two months before dropping out to pursue his comedy career. He started out at various improv clubs in Los Angeles, including The Improv in Hollywood and The Ice House in Pasadena. In 1984, he became the first $100,000 grand champion winner in the comedy category of the TV show "Star Search." This led to his first appearance, at age 23, on "The Tonight Show" starring Johnny Carson, making him one of the youngest comedians ever to perform on the show. His appearance with Carson brought Garrett a lot of national attention, and soon he was appearing as an opening act for such headliners as Diana Ross and Liza Minnelli. He also worked in Las Vegas with Frank Sinatra, David Copperfield, Smokey Robinson, Sammy Davis, Jr., the Beach Boys, and Julio Iglesias.

After achieving a strong measure of success with stand-up comedy, Garrett decided to change gears and try his luck with performing on TV. He was featured on Family Feud during Ray Combs's tenure during a Funny Men vs. Funny Women week during November sweeps. He then appeared in the short-lived summer comedy "First Impressions" (CBS, 1988), in which he was a divorced father who makes a living doing impressions and "The Pursuit of Happiness" (NBC, 1995-96), in which he was the hero's gay best friend. Though prior to these roles, Garrett had also had a minor part on Transformers, voicing the Decepticon base Trypticon in season three. He soon won the role of Ray Romano's brother Robert Barone on the long-running comedy hit "Everybody Loves Raymond." Garrett's distinctive deep voice has landed him notable work as a voice actor, such as on the animated series 2 Stupid Dogs, A Bug's Life, and Finding Nemo. He also provided the voice of Hulk Hogan in the World Wrestling Federation Rock 'N' Wrestling cartoons of the 1980s. His role in Everybody Loves Raymond has earned him five Emmy nominations and the 2002, 2003 and 2005 Emmy Awards for Best Supporting Actor in a Comedy. In 2003, he was also nominated for the Emmy for Outstanding Lead Actor in a Miniseries or a Movie for Gleason. With his Raymond castmates, he won the 2003 Screen Actors Guild Award for Outstanding Performance by an Ensemble in a Comedy Series. He won the fifth season championship of Celebrity Poker Showdown, and played in the 2005 World Series of Poker.

In 1998, Garrett proposed to his then girlfriend Jill Diven on the set of "Everybody Loves Raymond" and they were married on May 18, 1999. Their first child, Maxwell Bradley Garrett, was born on October 14, 1998 before the couple was married; their second child, daughter Hope, was born in January 2000.

Garrett was hoping to do a spinoff with his character Robert Barone from "Everybody Loves Raymond" when the show ended its nine-year run on TV in 2004, but he withdrew in October 2005 due to inaction from CBS that led to a number of the writers from "Raymond" leaving and taking other jobs.

In 2005, Garrett appeared on Broadway playing Murray the Cop in the revival of Neil Simon's "The Odd Couple" with Nathan Lane and Matthew Broderick.

Garrett currently lives in Los Angeles, California, with his wife and two children.