Grenier's mother, who was an announcer on a Polish radio program, met his father when he was working as a sound engineer at WBNX in the Bronx in the late 1930s. He is a graduate of Ann Arbor Pioneer High School.
He was a regular cast member on C-16 from 1997 to 1998. He appeared in the first season of the television show 24 as Carl Webb; played Andy Cramed, the gambler who brought the plague to town, on Deadwood; and appeared in several episodes of Law & Order.
In 2010, he was cast on the television series The Good Wife as David Lee, a senior attorney, a role that soon became part of the recurring ensemble. He was promoted to series regular at the start of the fifth season in September 2013.
Grenier has also had a prolific career in film. Notably, he played Edward Norton's boss in Fight Club and Mel Nicolai in Zodiac, both David Fincher films. He appeared in the 1988 film Talk Radio as finance guru Sid Greenberg, a role he played in the original stage version of the script. In the film Twister, he played Eddie, Dr. Jonas Miller's assistant. He played Mr. Reilly, one of the Callahan Auto Parts associates, in Tommy Boy. He appeared in Donnie Brasco as a marriage therapist. He played the role of Professor Cardiff in the 2006 horror film Pulse.
In 2009, he appeared on Broadway opposite Jane Fonda in 33 Variations, earning him a Tony Award nomination.
