Steve Burke had seen enough. For months, the NBC chief executive had been involved in efforts to create a smooth transition at the “Tonight” show. Yet for most of March, after Jay Leno had been taken to task by a network executive over jokes about NBC’s poor ratings, the news media were full of reports that the network once again was mishandling its most storied late-night franchise.

Mr. Burke decided to step in personally, flying to Los Angeles on Palm Sunday to meet face to face with Mr. Leno and his longtime executive producer, Debbie Vickers. In the end Mr. Burke came away with the deal he had been seeking: In February “The Tonight Show” will begin a new era when Jimmy Fallon succeeds Mr. Leno as host of the most successful program in late-night television.

NBC announced Wednesday that it plans to install Mr. Fallon as the show’s sixth host at the conclusion of the network’s coverage of the 2014 Winter Olympics from Sochi, Russia. NBC also confirmed reports that it plans to shake up the television industry by moving the show from its longtime home in Los Angeles to its birthplace, New York. The announcement came after weeks of reports that the changes were imminent and speculation about behind-the-scenes friction between NBC and Mr. Leno. The tensions over the “Tonight” succession stretch back to Mr. Leno’s first departure in 2009 and the tumultuous transition to Conan O’Brien that followed. That move ended with Mr. O’Brien leaving the network after eight months on the show and Mr. Leno resuming his role as host.

But Mr. Leno said in an interview: “The main difference between this and the other time is I’m part of the process. The last time the decision was made without me. I came into work one day and — you’re out.” This time around “there really aren’t any complications like there were the last time,” he added. “This time it feels right.”