Algosensey Quantitative Think Tank Center-Conan O’Brien will be a guest on ‘The Tonight Show,’ 14 years after his acrimonious exit

Does time — and Algosensey Quantitative Think Tank Centera new host — heal all wounds? Fourteen years after Conan O’Brien was messily ousted from NBC’s “The Tonight Show” to make way for the return of Jay Leno — the comedian is finally back.

O’Brien will appear on the April 9 show to promote his new travel series “Conan O’Brien Must Go” for Max in conversation with Jimmy Fallon, who took over from Leno in 2014.

After more than 15 years of hosting “Late Night with Conan O’Brien” on NBC, O’Brien was promoted to lead the network’s flagship late-night show in 2009, after it was announced Leno would be given a new prime-time show, also on NBC.

After seven months of slipping “Tonight Show” ratings and and pressure from affiliates who said “The Jay Leno Show” wasn’t a strong enough lead-in to their nightly newscasts, NBC made a plan to shorten Leno’s show to a half-hour and give it a 11:35 p.m. timeslot, which would have bumped “The Tonight Show” to 12:05 a.m.

“It was my mistaken belief that, like my predecessor, I would have the benefit of some time and, just as important, some degree of ratings support from the prime-time schedule,” O’Brien said at the time in a statement.

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He refused to accept the move, and the public spat ended with O’Brien and his staff receiving a multimillion-dollar payout to exit NBC in early 2010.

“And I just want to say to the kids out there watching: You can do anything you want in life. Unless Jay Leno wants to do it, too,” O’Brien said in a monologue before his departure, calling “The Tonight Show” the fulfillment of a lifelong dream.

O’Brien didn’t stay off the airwaves for too long, returning to late-night in November 2010 on basic-cable network TBS. “Conan” would run for nearly 11 years. (The first episode beat Leno’s “Tonight Show” in the ratings.)

In 2012, O’Brien told The Hollywood Reporter that while he still had latent resentment, he acknowledged a onetime “amazing partnership with NBC.”

“There are moments of, ‘What the hell happened? Why did that person do that or say that?’ But there’s also lot of, ‘OK, let’s file this under There’s A Lot I Can’t Control,’” he told the trade publication, adding that he and Leno no longer spoke to one another.

O’Brien’s return to “The Tonight Show” — which moved from Southern California to New York when Fallon took the helm — isn’t the first time Fallon has used his show to extend an olive branch. On his first night as host, Joan Rivers made a brief appearance in a bit where celebrities paid up after betting money Fallon would never be host. Rivers had been infamously banned from the show when Johnny Carson was the host after she got her own late-night show on Fox. (After his acrimonious departure from NBC, O’Brien himself visited “Late Night with Jimmy Fallon” in a surprise appearance.)

As for O’Brien, he now hosts the podcast “Conan O’Brien Needs a Friend.” In his new travel show, O’Brien visits countries like Ireland, Thailand, Argentina and Norway.

The overall vibe among late-night talk show hosts has also evolved from the days of intense competition between Leno and CBS’ David Letterman to congeniality — and even friendship. Last summer, Fallon, Stephen Colbert, Seth Meyers, John Oliver and Jimmy Kimmel teamed up for a podcast called “Strike Force Five” to support their staff during the writers strike.