Noonan was born in Greenwich, Connecticut, the son of Rosaleen Noonan, a dentist, and Tom Noonan, a jazz musician. He has an older brother, John Ford Noonan, a playwright, and two sisters, Barbara and Nancy.
Noonan started working in theatre (appearing in the original Off-Broadway production of Sam Shepard's play Buried Child), but in the 1980s he began working in film. At 6 feet, 5 inches (196 cm), Noonan's imposing presence is probably responsible for his tendency to be cast as menacing villains, as in RoboCop 2, Last Action Hero, Manhunter, and The Pledge. His height was used for comic effect in "The Moving Finger," the series finale of the horror anthology Monsters (several episodes of which he also directed and wrote). In 1986, Noonan played Francis Dolarhyde, a serial killer who kills entire families, in Michael Mann's Manhunter, the first movie to feature Hannibal Lecter. Another supporting role, and another collaboration with director Michael Mann was in 1995, as Kelso in Heat. He also played the Frankenstein monster in The Monster Squad. During the 1990s, he wrote various plays, including two that he made into movies, What Happened Was... (1994) and The Wife (1995). In the 2000s, Noonan appeared in various other movies, including a widely praised role as Sammy Barnathan in Synecdoche, New York, Charlie Kaufman's directorial debut. Most recently, he originally voiced one of the Wild Things in director Spike Jonze's Where the Wild Things Are, but was replaced by Chris Cooper.
Noonan has also made numerous appearances in television series, including The X-Files (in the much-praised 1996 episode "Paper Hearts" that was written specifically for him), Law & Order: Criminal Intent, Law & Order: Special Victims Unit, Tales from the Darkside and CSI: Crime Scene Investigation (in which he starred alongside William Petersen, who played his nemesis, Will Graham, in Manhunter), and Detective Victor Huntley in Damages. He recently appeared on Louie as a doctor who takes the young Louie through the crucifixion in graphic anatomical detail. He also portrayed the Reverend Nathaniel Cole in the AMC original series Hell on Wheels. In 2015, Noonan voiced all of the supporting characters in Duke Johnson and Charlie Kaufman's stop-motion comedy-drama film Anomalisa, for which he won the San Diego Film Critics Society Award for Best Supporting Actor.