NEW YORK — Stephen Colbert began his tenure as host of the CBS “Late Show” Tuesday with a tribute to predecessor David Letterman, a brief conversation with rival Jimmy Fallon and a surprise cameo from Comedy Central buddy Jon Stewart.

After months of buildup, the former host of “The Colbert Report,” returned to late-night TV by gorging on Donald Trump jokes and noting his transition from playing the character of a cable TV blowhard to being himself.

“With this show I begin the search for the real Stephen Colbert,” he said. “I just hope I don’t find him on Ashley Madison.”

Colbert was joined by actor George Clooney and Republican presidential candidate Jeb Bush. He completes the remake of late-night network television from the days of Letterman and Jay Leno to the two Jimmys (Fallon and Kimmel) and himself.

Colbert showed a picture of the now-retired Letterman, saying he bowed to no one as a Letterman fan.

“We will try to honor his achievement by doing the best show we can and occasionally making the network very mad at us,” Colbert said.

The guest list for Colbert’s first week indicates he plans to get beyond the typical show biz patter of many talk shows. Vice President Joe Biden will visit Thursday and the CEOs of Tesla Motors and Uber also will make appearances. Comic Amy Schumer, actress Scarlett Johansson and author Stephen King are on the schedule.