Thompson was born and raised in Atlanta, Georgia, the son of Fletcher and Elizabeth Ann Thompson. He has two siblings, an older brother and a younger sister. He began acting at age 15, appearing in the school play The Gingerbread Duck. He auditioned for a theatre company The Youth Ensemble of Atlanta (YEA). One of his earliest roles was as an entertainment reporter for CNN's "Real News for Kids", and he would go on to star in All That, and Kenan & Kel. While Kenan attended Tri-Cities High School, a Visual and Performing Arts Magnet School in East Point, Georgia, he began filming his first movie, D2: The Mighty Ducks.
Kenan has starred in several films including Good Burger, based on the All That sketch of the same name, and Fat Albert, in which he played the title character. He has also had supporting roles in the movies Heavyweights, D2: The Mighty Ducks, D3: The Mighty Ducks, Love Don't Cost a Thing, Barbershop 2: Back in Business, My Boss's Daughter, and Snakes on a Plane. Thompson had a recurring role on The Steve Harvey Show as Junior, with co-star Kel Mitchell.
In 2009, Thompson was a regular voice actor in the Fox cartoon series, Sit Down, Shut Up, portraying Sue Sezno, who, as evidenced by her last name, always says no. The series premiered on April 19, 2009, but was canceled after only four episodes due to low ratings and less than favorable reviews. Thompson provided the voice for the LeBron James puppet in Nike's MVP "Most Valuable Puppets" commercials, which were produced to be shown throughout the 2009 NBA Playoffs. Thompson also guest starred on the USA Network TV show Psych in Season 4's "High Top Fade Out" (episode 7). He played an estranged college singing buddy of the character Gus. In 2011, he briefly returned to Nickelodeon, as he guest starred in "iParty with Victorious", a crossover episode of TV sitcoms "iCarly" and "Victorious". Thompson is the current host of TeenNick's 1990's programming block, The '90s Are All That.
In 2015, Fandango announced that Thompson would play their brand character, fictional character Miles Mouvay. Thompson will play Mouvay in 18 videos, eight 30-second commercials, and a few comedic skits.
On September 23, 2015, Thompson appeared on The Tonight Show Starring Jimmy Fallon alongside former All That co-star Kel Mitchell in which they reprised their iconic Good Burger roles as "Ed" and "Lester Oakes, Construction Worker".
Thompson returned to sketch comedy when he joined the cast of Saturday Night Live in 2003, becoming the first SNL cast member to be born after SNL's premiere in 1975 and the first SNL cast member to have been a cast member on children's comedy shows (the Nickelodeon sketch show All That and the Nickelodeon sitcom Kenan and Kel). Kel Mitchell, his comedy partner and close friend, also auditioned to be on SNL, but he didn't make the cut. Thompson was a featured player until 2005 (spanning the 29th and 30th seasons) and was promoted to repertory player at the beginning of season 31 (the 2005–2006 season).
Thompson has been a cast member on SNL for fourteen seasons, breaking the record for the longest-serving African-American cast member previously held by Tim Meadows, who stayed on the show for ten seasons. Thompson became the most senior cast member in the 2013-14 season, following the departure of Seth Meyers. He is also the longest-tenured cast member in the show's history, surpassing Darrell Hammond in 2017-18 season, and is also the second-oldest current cast member after Leslie Jones (born 1967). Thompson also holds the record for most celebrity impressions performed on the show, performing 122, beating Hammond's previous record of 107.
Thompson married model Christina Evangeline on November 11, 2011. Together, they have one child, a daughter, born in 2014.