Elliott has written three books spoofing history or pseudo-history. Daddy's Boy: A Son's Shocking Account of Life with a Famous Father is a comedic fictionalized biography about growing up with his famous father, spoofing Christina Crawford's Mommie Dearest. The Shroud of the Thwacker is a historical novel about Elliott's investigation of a serial killer in 1882 New York City, spoofing London's infamous Jack the Ripper case. Into Hot Air tells the story of Chris climbing Mount Everest with a group of celebrities tagging along to underwrite the trek as he investigates his Uncle Percy's failed Everest expedition.

Elliott was born in New York City, and is the youngest of five children of Lee (née Peppers), a model and TV Director, and Bob Elliott, who was part of the successful comedy team Bob and Ray. He grew up on the Upper East Side. He attended the National Theater Institute at the Eugene O'Neill Theater Center in the spring of 1979.

Elliott became known in the mid-to-late 1980s, when he was a Writer and performer on Late Night with David Letterman, playing an assortment of recurring quirky, oddball characters. His characters on the show included:

Elliott has been married to Paula Niedert since 1986. Niedert worked as a talent coordinator on Late Night with David Letterman when they met. They have two daughters: Abby and Bridey. Abby was a cast member of Saturday Night Live from 2008 until 2012, making her the first SNL cast member to be the child of a past cast member. His father Bob Elliott of the popular comedy duo Bob & Ray co-starred on a SNL Christmas episode in the 1978–1979 season fourth season, making for three generations of Elliotts on SNL.

In 1990, Elliott created and starred in his own sitcom, which was called Get a Life, about a 30-year-old paperboy named Chris Peterson who lived at home with his parents. Elliott's real-life father, Bob Elliott, appeared in the show as Chris' father. The January 1999 issue of TV Guide called the "Zoo Animals on Wheels" episode the 19th funniest TV moment of all time.

In 1993, Elliott teamed up with Producer Brad Hall and directed a series of critically acclaimed short films that Elliott showed when appearing on Late Show with David Letterman.

Elliott became a cast member of Saturday Night Live in 1994. Also that year, Elliott starred in his first movie—entitled Cabin Boy—which also featured a short appearance by Elliott's old boss, David Letterman, and was produced by Tim Burton. He was nominated for a Razzie Award as Worst New Star.

In 2007 Elliott again began appearing on the Late Show with David Letterman with fellow former Letterman Writer Gerard Mulligan. On average, these bits appeared once per month.

His other television credits include the chowder taster on Throwdown with Bobby Flay, airdate 09/02/09, and the voice of Dogbert on the short-run show Dilbert for UPN. He played a serial killer in the series Third Watch in episodes 5, "The Hunter, Hunted," and 6, "Greatest Detectives in the World" from season six. He played the role of Peter in the last three seasons of Everybody Loves Raymond and a role in a semi-autobiographical sitcom pilot for CBS, entitled You've Reached the Elliotts, playing a man who tries to balance a modest show Business career with his home life. As of 2009, Elliott has played the estranged father of How I Met Your Mother character Lily Aldrin, whose relationship has strengthened as the show has progressed. As well as multiple appearances on The King of Queens, Elliott made guest appearances on the Late Show, That '70s Show episode "2000 Light Years From Home", and According to Jim. Since February 3, 2011, Elliott has starred in the Adult Swim series Eagleheart, produced by Conan O'Brien's production company, Conaco.

In 2015, he had a guest role on an episode of NBC's Law and Order: Special Victims Unit and began a starring role as Roland Schitt in Schitt's Creek.

Elliott was also in an Avocado's from Mexico commercial in February 2018.