The "Daily Show" host saluted his old pal and former colleague last night after Colbert was officially named as the heir to David Letterman.
Stewart called his time with Colbert "one of the great pleasures" of hosting the show.
Colbert parlayed his role on the "Daily Show" into his own Comedy Central program, "The Colbert Report," which he's hosted since 2005 in character as a blowhard conservative pundit. The character will be dropped when Colbert shifts to CBS to assume the "Late Show" next year.
"So, the exciting news today is I no longer need a cable subscription for the privilege of watching Stephen Colbert," Stewart said.
Stewart hailed Letterman as "the comedian-broadcaster who is the best there ever was," but said Colbert is a worthy successor.
"And here's the exciting thing for me: I think Stephen Colbert is up for the challenge."
"There is no greater joy than seeing a genuinely good man who works as hard as he can every day and deserves all the success in the world actually get that success," he added. "So for Stephen, we're just thrilled."
In an interview he gave to Vulture this week on the eve of CBS' announcement, Stewart said Colbert would be an "amazing" choice to replace Letterman. The network clearly agreed, as Colbert was reportedly the top choice pretty much from the moment Letterman announced his retirement.
Stewart and company also paid tribute on the "Daily Show's" website, devoting a large portion of the page to some of Colbert's funniest clips.