After achieving enough stand-up success to carve out a living — because “at that point, you realize, ‘Oh, I’m going to have to do this now or end up living behind the bus station’ ” — Mr. Oliver decided to kill his safe established act and make a new start with jokes about current events. “I went to a pub in Birmingham, and for some reason they didn’t respond well to jokes about the I.M.F. I remember being on the bus home and it felt great — apart from the crushing failure, it felt great.”

A break came when he worked with the Scottish satirist Armando Iannucci (creator of “Veep” for HBO) on a radio program commenting on British politics. Ricky Gervais heard Mr. Oliver, and when asked by Mr. Stewart if he knew any young talent in Britain, suggested him, though the men did not know each other. “I owe him big,” Mr. Oliver said.

Among the highlights of his ensuing career at “The Daily Show, probably the most memorable for him was covering the 2008 Republican Convention in St. Paul. As his usual obnoxious correspondent, he was at risk because he could not afford to get arrested for anything — deportation loomed. So when he wandered into a restricted area and was pursued by security, he sought refuge among some veterans invited by pro-military politicians. The one who helped Mr. Oliver hide out was a female vet, Kate Norley. He was grateful, took down her email and married her three years later.

He is still a British citizen, though now his resident status is secure as the spouse of an American. His life has been such a whirlwind, the clothes and other personal items he stowed away in 2006 remain exactly where they were, in a storage unit in London. “It’s either there or it’s been robbed or there’s been a fire,” he said.

Notably, as Mr. Oliver gets his shot to score, the playing field is surprisingly open. On Sunday night at 11, he will be the only late-night comic at work.

“There’s nothing else like this on Sundays,” Mr. Lombardo of HBO said. “I wish I could say that was the first thing I thought. But it wasn’t.” And he added, “We knew that Sunday is premium real estate for us.”