"Congratulations Jimmy," Leno said in a statement. "I hope you're as lucky as me and hold on to the job until you're the old guy. If you need me, I'll be at the garage."
Check out other stars who deserve a late-night talk show
Fallon added with his own humorous sentiment: "I'm really excited to host a show that starts today instead of tomorrow."
NBC also confirmed reports that The Tonight Show will move back to its original home in New York when Fallon takes over. The Tonight Show debuted in the Big Apple with Steve Allen in 1954 before Johnny Carson moved it to Burbank, Calif., in 1972.
Lorne Michaels, who currently produces Late Night with Jimmy Fallon, will executive-produce Fallon's The Tonight Show. Plans for Fallon's Late Night successor are in development, NBC added. Fallon's former Saturday Night Live co-star Seth Meyers is reportedly the frontrunner for the gig.
"We are purposefully making this change when Jay is No. 1, just as Jay replaced Johnny Carson when he was No. 1," Steve Burke, chief executive officer of NBCUniversal, said in a statement. "Jimmy Fallon is a unique talent and this is his time. I'm thrilled he will become the sixth host of The Tonight Show at exactly the right moment, in conjunction with our coverage of next year's Winter Olympic Games from Sochi, Russia."
NBC's announcement comes a month after news first broke of NBC's late-night plans and only three years after Leno, who took over for Carson in 1992, returned to the show following his ill-fated prime-time show and Conan O'Brien's departure from The Tonight Show.