Stephen Colbert’s stint as a Comedy Central host ended on Thursday night, and assuming that they were part of the audience, his new bosses at CBS should have gone to bed with big broad grins on their faces.

As several of his latenight contemporaries pointed out in a New York Times piece devoted to Colbert’s farewell, the fact the host was able to maintain the character — and improv through interviews every night while inhabiting it — suggests a well-spring of inventiveness and quickness that will serve him inordinately well in his new gig.

If that seems like an obvious point, it’s been lost on some of those who have wondered about how well Colbert will fare once he retires his blowhard cable-news host persona and has to be plain old Stephen Colbert.

The final episode wasn’t perfect — the weight of expectations appeared to foster throwing in some unnecessary bits — but it reflected all the things that have been such assets to Colbert through the years: A willingness to be silly, an inordinate grasp of pop culture, an ability to get guests to do amusing things (even Congressmen), and an inherent warmth, which was put to grand use in his star-studded (and then some) rendition of “We’ll Meet Again.”

Colbert never mentioned CBS during the course of the evening, but the underlying message of that song was clear: Yes, sure, we can all make a big deal about his final episode, but he’ll be back — hitting up all the same folks to be guests on his new show — soon enough.

There was also a taste of the not-“Colbert Report” version in the very closing moment, a clip that showed Colbert and Jon Stewart riffing as they giggled their way through the toss from one show to the other. That conceit was eventually abandoned, tacit recognition that Colbert could stand on his own and no longer needed a direct assist from the program and performer who helped launch him.

When CBS announced that Colbert would replace Letterman, it felt like exactly the right person to pick up Letterman’s mantle as, if not always necessarily the highest-rated host, the one who is generally the most influential and admired by his peers — a factor that always made Letterman a sought-after destination for guests, even if he chafed at trailing Jay Leno. Letterman’s blessing also suggests Colbert will enjoy a smooth, drama-free transition, which wasn’t true when Leno came and went — and went again.

“If this is your first time tuning in to ‘The Colbert Report,’ I have some terrible news,” Colbert deadpanned near the outset.Terrible, perhaps, only in the sense that it’s a shame to see a good thing come to an end, but the future for Colbert and his fans looks bright. And for once, that’s not just truthiness; it’s the actual truth.