News of Leno's departure was expected, especially since the veteran host recently began making jokes at the expense of NBC bosses in his nightly monologues, reported Washington Post.
Leno remains the most-watched late-night host overall, but NBC is betting on Fallon to draw more youthful viewers in future.
"We are purposefully making this change when Jay is No 1, just as Jay replaced Johnny Carson when he was No 1. Jimmy Fallon is a unique talent and this is his time," NBC Universal chief executive Steve Burke said in a statement.
In 2009, NBC installed Conan O'Brien as host of The Tonight Show, only to controversially reinstate Leno following a ratings slump.
Fallon's current show Late Night recently enjoyed a viral coup with Michelle Obama dancing alongside Fallon in a clip entitled 'The Evolution of Mom Dancing'.
There is widespread speculation that Fallon will be replaced by his fellow Saturday Night Live alumnus Seth Myers.
When Fallon replaces Leno, The Tonight Show will also be broadcast from New York for the first time since it moved to Los Angeles more than 40 years ago.