“The Tonight Show” will begin a new era in February when Jimmy Fallon succeeds Jay Leno as host of the most storied and successful program in late-night television. NBC plans to announce on Wednesday its plan 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 is to confirm reports that it plans to shake up the axes of the television industry by moving the show from its longtime home in Los Angeles to its birthplace, New York.