Last Updated Apr 4, 2014 2:00 PM EDT
"Dave's the greatest. One of the true innovators in TV history. He's made all of us better," "Tonight Show" host Jimmy Fallon said in a statement to The Hollywood Reporter.
On "Late Night," host Seth Meyers also praised Letterman, who launched the show in 1982.
"I grew up on David Letterman," Meyers said. "I remember we used to memorize Top Ten lists so we could tell them on the bus the next day."
He added: "There are a lot of things I can't believe about the fact that I get to do this job. The thing I truly can't believe more than all of the others is -- 'Late Night,' this was David Letterman's show. If it wasn't for David Letterman, this show wouldn't exist. If I wasn't for David Letterman I wouldn't' be here."
Jimmy Kimmel, Andy Cohen and Ellen DeGeneres were among those who took to social media to talk about Letterman and his legacy.