04/23/2014 04:43 am ET Updated Apr 23, 2014

Stephen Colbert And David Letterman Talk 'Boobs'

Stephen Colbert paid his first visit to the "Late Show" since CBS announced that he'll be taking over hosting duties from David Letterman next year.

"He just stopped by to sign the lease," Letterman said during his monologue on Tuesday night.

Letterman said he was "thrilled" that Colbert would be his replacement.

"They could have just as easily hired another boob like me," he said. "But they didn't."

"They hired a boob like me," Colbert replied. "Every boob is like a snowflake, Dave. We're all unique in our own way."

The two then posed for a selfie, which Colbert posted to Twitter with a #boobs hashtag:

Colbert also recounted turning down an internship with Letterman in 1986 and then applying to be a writer on the show in 1997. He submitted a packet with a writing partner that included a "Top Ten" list. Since it was Christmastime, it was the "Top Ten Cocktails for Santa," including a drink called "No Room at the Gin." That's when you chill a martini glass and "fill it with gin until there is no room for anything else."

You can see the rest in the clip above.

Letterman said he liked that Colbert explained each joke in his "Top Ten" list.

"You don't explain your jokes?" Colbert asked.

"No, we gave up on that back in '97," Letterman replied.



Stephen Colbert's Journey To The "Late Show"