In 2004, as Jimmy Fallon was leaving “Saturday Night Live” after a six-year run creating sketch characters and sharing the “Weekend Update” desk with Tina Fey, Lorne Michaels floated an idea.

Michaels, Fallon’s patron at “SNL” and the show’s executive producer, had a hunch that this comedian’s future did not lie in Hollywood and movies, which he wanted to pursue, but on a traditional late-night talk show.

“I always thought that was the best use of his talents,” Michaels said. “There are very few people who can do that job. I always say there are a hundred U.S. senators and eight people with their own show.”

That instinct has paid off for both men: Starting this week, Fallon, fresh from almost five years of very-well-received work at “Late Night” on NBC, becomes the star of that network’s venerable “Tonight Show,” with Michaels overseeing it as executive producer, now in control of all the most important properties on the NBC late-night landscape.

“I think he’s ready for the moment,” Michaels said last week.

More than ready, Fallon is brimming with confidence after his apprenticeship at “Late Night,” which follows “Tonight.” In his stylized club of an office on the sixth floor of NBC’s Rockefeller Center headquarters, known as 30 Rock, Fallon, lanky, loose limbed and still boyish at 39, was bubbling with enthusiasm. “I’m supremely excited,” he said. “But I’m older. I’ve grown up. I was nervous at the start of ‘Late Night.’ Now I know I can do this show.”

NBC certainly believes he can — and that Fallon will be up to the daunting challenge of keeping “Tonight” relevant in the face of altered viewing habits, an upheaval in audience demographics and diminishing late-night profits. The network, for a second time, put together a plan to ease a reluctant (and still winning) Jay Leno out of the “Tonight” chair in favor of a new-generation star. (Leno’s last night was Feb. 6.)

The motive for the change was not purely economic, because “Tonight” is not the profit generator it once was. The show can still make money on a tighter budget, and Fallon will, at least for a time, make considerably less than Leno’s reported annual salary of about $20 million. (NBC imposed staff and salary reductions on Leno in 2012.)

For NBC, the move is more about maintaining a vital piece of its birthright than retrofitting an ATM machine. That is one reason Fallon will open his “Tonight” in an expensive, elegant renovated studio at Rockefeller Center. Still, to remain an essential part of American culture, “Tonight” required a generational change at some point, adjusting the focus from baby boomers to their millennial kids. Leno’s audience, while still the largest in late night, had steadily aged. The median viewer was below 50 in 2005; when Leno left the air this month, it had climbed to 57.8.

The network shows all have older audiences. At ABC, the median age for viewers of “Jimmy Kimmel Live!” is 54.2. Then there’s David Letterman, the CBS veteran who has the oldest viewership, with a median age of 58. That audience may expand and get even older, if he inherits some of Leno’s more traditional viewers, as he did for the eight months when Conan O’Brien (who had a considerably younger core audience) took over “Tonight.”

Though NBC clearly wants Fallon to hold onto the lead in total audience, the larger question is whether any of the network late-night shows can induce younger viewers to commit regularly. They tend to steer clear of traditional broadcasting, and they realize they can see Fallon’s best comedy bits the next day on YouTube.

Even with potent competition for younger viewers all over cable, from the likes of Jon Stewart and Stephen Colbert on Comedy Central and O’Brien on TBS, the host NBC is clearly most concerned about is Kimmel, who is 46. (The only female host in late-night is Chelsea Handler, 38, on E!) Fallon has posted steadily climbing ratings recently, but one underacknowledged reason NBC pushed for the change to occur now is that its executives did not want Kimmel to settle in for too long, taking the competition to the new platforms of online videos and social media. Adding Seth Meyers, 40, as the new “Late Night” host is another NBC move to reassert its late-night block as a continuing franchise, ready to continue its decades of dominance.

But change is always risky, and by almost every estimation, NBC is getting a different kind of host with Fallon, one who brings talents both new and old to the job.

The new is obvious: He has moved aggressively to take advantage of the increasing importance of Internet viewing of bits from late-night shows. Like Kimmel and O’Brien, Fallon has broken though with widely watched videos, like his recent “Born to Run” parody with Bruce Springsteen about Gov. Chris Christie’s traffic fiasco. It has had about 4 million views. That’s modest by Fallon’s standards. “The Evolution of Mom Dancing” with Michelle Obama is up to 17 million views. And a conversation with his pal Justin Timberlake, all in hashtags, has 21 million.