Being gracious doesn’t come naturally to David Letterman. So while he had already essentially provided his blessing to the choice of Stephen Colbert to replace him as host of “Late Show,” CBS execs were no doubt relieved after Tuesday’s program, in which the reigning host featured the host in waiting as a guest.

That’s not to say the interview was particularly smooth. At this point, unless he has someone who really engages him in the chair, there’s a sense Letterman does about as little research as possible, serving up the pre-interview questions with what feels like a sense of obligation.

Yet even with that, the rapport between the two made clear that Letterman embraces Colbert’s talent, and that Colbert doesn’t just idealize Letterman — as many comics of his generation do — as latenight’s most influential talent, but also has a long relationship with the host, albeit from afar. (On his own program, Colbert talked about missing college classes because he had stayed up watching Letterman’s “Late Night” in the 1980s.)

On Tuesday, Colbert told two illuminating anecdotes — having applied for a “Late Night” internship in 1986 (he got it, but passed because it didn’t pay) and submitting material to write for “Late Show” in 1997. He even brought along a pretty clever Top 10 list that he and his writing partner had submitted as a sample. (Letterman didn’t mind the drumroll, but expressed mock outrage when they flashed the Top 10 graphics on Colbert’s behalf.)

All told, Letterman’s demeanor was about as all-smiles an endorsement as one is apt to get out of the irascible host, while Colbert clearly looks like someone who views replacing Letterman with a reverence similar to what Letterman and Jay Leno harbored in regard to Johnny Carson on “The Tonight Show.” And if that wasn’t enough, their adorable selfie is one of those pictures that really is worth 1,000 words.

“He just dropped by to sign the lease,” Letterman quipped during the opening monologue.

As stiff as most signing ceremonies are, this one couldn’t have gone much better.