Kimmel has decided not to air a new episode that night on competing network, ABC. Instead, ABC will run a repeat of "Jimmy Kimmel Live."
"I have too much respect for Dave to do anything that would distract viewers from watching his final show," Kimmel told The New York Times, adding, "Plus, I'll probably be crying all day, which makes it hard to work."
Letterman lined up a slew of guests for his final days on the air, including George Clooney, Robert Downey, Jr., Will Ferrell, Tina Fey, Tom Hanks, Scarlett Johansson, Michael Keaton, Steve Martin, Bill Murray, Sarah Jessica Parker, Don Rickles, Julia Roberts, Jerry Seinfeld, Martin Short, Howard Stern, John Travolta, Bruce Willis, Oprah Winfrey, The Avett Brothers, Elvis Costello, Dave Matthews Band, Emmylou Harris, Norah Jones, Mumford and Sons and more.
The late-night talk show host made his debut on the "Late Show" on Aug. 30, 1993. His final episode will air May 20 -- after 6,028 late-night shows over 33 years on CBS and NBC.
Stephen Colbert will take over hosting duties.