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.
David @Letterman is the best there is and ever was.— Jimmy Kimmel (@jimmykimmel) April 3, 2014
David @Letterman announced he's retiring in 2015. It's been 31 incredible years. Television won't be the same without you, Dave.— Ellen DeGeneres (@TheEllenShow) April 3, 2014
Letterman broke the mold for not just Late Night, but TV itself. He's a vanguard- his influence is seen all over the dial today. What a run!— Andy Cohen (@Andy) April 3, 2014
I love Letterman but I am really excited about what this could mean for the diversification of late night. Trying not to be a pessimist...— Lena Dunham (@lenadunham) April 3, 2014
Obvi will miss Letterman and his gorgeous tooth scenario/general brilliance— Lena Dunham (@lenadunham) April 3, 2014
Important to note: Letterman is not dead. That said, I will miss him and his program once he is gone...from late night TV— Colin Hanks (@ColinHanks) April 3, 2014
Mr. Letterman, you have always been the best. I've had more fun on your show and you've been a class guy all the way. Enjoy ur final days.— jason alexander (@IJasonAlexander) April 3, 2014
Respect to Letterman - but it's the two JIMMY'S time- and I couldn't be happier. They are the future of Late Night.— John Stamos (@JohnStamos) April 4, 2014