The deal was done by the time Jonathan Klein, the president of CNN/U.S., flew to Los Angeles and had lunch with Larry King on Tuesday.

Mr. King would be stepping down from his daily talk show sometime in the fall — no later than November — paving the way for a new CNN program at 9 p.m. for the first time in 25 years. A new contract would allow Mr. King to come back on CNN for occasional specials.

At lunch, after some chit-chat about the Dodgers and the Yankees (Mr. King sides with the Dodgers; Mr. Klein, the Yankees), talk turned to the future.

“He already had the wheels turning about what these specials could be,” Mr. Klein recalled in a telephone interview Tuesday. He conjured up Mr. King’s voice: “Big! Ground-breaking! Global!”

“At this point, he’s thinking far and wide and big,” Mr. Klein added. Mr. King said on his show that the specials would be about “major national and international subjects.”

The terms of his new contract are unknown, but Mr. Klein said Mr. King would be hosting specials for several years.

Asked what he would say to people who suspect that the change wasn’t all Mr. King’s doing, he said, “I saw it happen, so I can tell you. This is what Larry wants to do. He’s embracing it. He is naturally wistful about the change, but at the same time, he’s very excited about the new opportunities.”

After lunch, Mr. King picked up his children at school. That evening, he told tell viewers that the end of “Larry King Live” would allow “more time for my wife and I to get to the kids’ little league games.”

And then he talked with the comedian Bill Maher, who he said he had invited especially for the announcement. Mr. Maher said he missed Mr. King already, prompting a reminder that “I will be here for a while.”

“Then I will be doing specials and you will see me in other places,” Mr. King said. “Remember, I’m free.”