On Thursday, the rumor mill was put to rest when the network announced that Stephen Colbert had been given the gig.
Media pundits then began to wonder whether the Comedy Central funnyman would retain his satirical persona from "The Colbert Report," a show he's hosted on the cable network since 2005 and will end later this year.
Colbert, 49, has played the role of an ultra-right wing talk-show host, a character he's almost never broken from during his time on Comedy Central.
In an interview Thursday with CBS Radio's Dan Raviv, CBS Chairman and CEO Les Moonves said that "Late Show" viewers can expect to see Colbert be himself in his new role.
"The character that he's currently doing on Comedy Central will end by the end of the year at Comedy Central and then he will come back on CBS as Stephen Colbert," Moonves said. "Those of us who know him know that he is multi-talented and can go way beyond the character that he is currently playing. And we're looking forward to that."
A public guessing game erupted last week about which TV personality would succeed Letterman, with names like Ellen DeGeneres and Colbert's Comedy Central lead-in Jon Stewart brought up, but for Moonves, picking "The Colbert Report" host for the high-profile role was a no-brainer.
"When David announced that he was retiring, obviously there were a lot of possibilities and a lot of choices," Moonves said, later adding, "But when we took a step back, the one that really stood out was Stephen."
Moonves said that he and his wife, "The Talk" co-host Julie Chen, are big fans of "The Colbert Report" and he looks forward to working with the funnyman as he transitions to CBS. He added that Letterman, 66, is also a Colbert fan.
"When we went back to Dave to get his blessing, he loved the choice," Moonves revealed.
Tell us: Are you happy with Colbert as the new "Late Show" host?