Thompson was born and raised in Atlanta, Georgia, the son of Fletcher and Elizabeth Ann Thompson. He has one sibling, Kevin Thompson. He began acting at age 15, appearing in the school play The Gingerbread Duck. 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.
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, 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.
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 only Thompson was hired. 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 eleven 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 is now the senior cast member on the show, after Fred Armisen and Seth Meyers left the show. He is also the second-oldest current cast member after Bobby Moynihan (born 1977). Thompson also holds the record for most celebrity impressions performed on the show, performing 108, beating Darrell Hammond's previous record of 107.