Parnell was born in Memphis, Tennessee, to a Southern Baptist family. His father, Jack Parnell, was a radio personality in Memphis. He attended the Southern Baptist Educational Center, and graduated from Germantown High School. He decided to pursue acting as a career at age 17 and set his sights on being a theater actor. He attended the University of North Carolina School of the Arts where he received his BFA in Drama. He moved to Houston, Texas after college to do an apprentice actor program for a season at the Alley Theatre, but did not get asked back to join the company. He became momentarily disenchanted with acting, and returned to his hometown and taught high school for a year. He moved to Los Angeles and auditioned for the Groundlings in 1992.

While performing as a company player with the Groundlings for a number of years, Parnell began doing commercials and getting guest roles on various sitcoms, such as Seinfeld and Murphy Brown. He was hired to join the cast of Saturday Night Live as a featured player, and debuted on the show on September 26, 1998. He was promoted to repertory player the following season. In the summer of 2001, because of budget cuts and the hiring of four new cast members, Lorne Michaels was required to dismiss two cast members; he chose to lay off Parnell and Jerry Minor over Horatio Sanz, Rachel Dratch, and Maya Rudolph, but Parnell was rehired in the middle of the following season.

In mid-2006, Michaels announced that four cast members would be laid off due to budget cuts, but he did not say whom. On September 22, 2006, it was announced that three cast members had been laid off: Parnell; Horatio Sanz; and Finesse Mitchell. This effectively made him the only SNL performer to have been released twice by Lorne Michaels, although Parnell did say in a 2008 interview with The Sound Of Young America podcast that he was okay with being let go this time, as he was considering leaving after that season anyway, adding that he probably would have stayed one more season had he been asked back. He had been with SNL for eight seasons; at the time only four people (Darrell Hammond, Tim Meadows, Kevin Nealon, and Al Franken) had been cast members longer. He has since made uncredited cameo appearances on the show, including parodying newscasters Tom Brokaw, Jim Lehrer, and Bob Schieffer. Parnell and his former SNL castmate Horatio Sanz starred together in Big Lake, a 2010 sitcom on Comedy Central from executive producers Will Ferrell and Adam McKay.

Since 2013, Parnell has voiced Jerry on the Adult Swim series Rick and Morty.

On March 16, 2018, Parnell was cast in the main role of Wayne on the CBS sitcom Happy Together.