Stephen Colbert Hilariously Riffs on Replacing David Letterman

04/11/2014 at 01:15 PM EDT

Stephen Colbert is so happy about landing the job as host of the Late Show on CBS, all he can do is get laughs about it.

Speaking to the audience on The Colbert Report, which Comedy Central executives say will end its run in eight months, Colbert, 49, paid homage to his Late Show predecessor.

"I'm going to miss this good man. Dave has been on the air my entire adult life," he says in the voice of his famous conservative character. "I learned more from Dave than I did from going to my classes."

Getting thunderous applause from a knowing audience, Colbert deadpans: "I do not envy whoever they try to put in that chair. Those are some huge shoes to fill, and some really big pants."

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