That moment, Mr. Colbert said, was possible only because of the live shows he had done in the previous months.

“That’s when it changed for us,” he said. “And that’s when it started to feel like when you walk off the stage and say, ‘God, what a great freaking job, that I get to do this!’” (He used slightly more colorful language.)

Two weeks into Mr. Trump’s presidency, Mr. Colbert beat Mr. Fallon for the first time. Beyond the political moment, however, Mr. Colbert said he felt more comfortable on the Ed Sullivan Theater stage than ever before.

“I always had to keep a certain amount of distance as the character,” he said of his time at Comedy Central. “I always had to be a little of a facsimile of me that they were getting — obviously because I was playing somebody named me who wasn’t me, but even on top of that there was a little bit more of a distance from the audience.”

Mr. Colbert runs out onto the stage every night these days, and high-fives audience members in the front row. A cameraman circles around him, and Mr. Colbert looks directly into the lenses and says, “Hey.” Mr. Licht said Mr. Colbert had started doing that on his own just about three months ago, a brief, intimate moment between the host and the viewer, watching at home, right before bed.

“I’m so much more comfortable on my feet now,” Mr. Colbert said. “I’m a quicker and better writer. I am more comfortable being myself in front of an audience. I like this new relationship with the audience.”