Going into the final round, England's Fitzpatrick was the only player who could have denied the in-form Olesen his Ryder Cup debut, but he could not mount a victory charge, finishing on 16 under after a fourth-round 66.
Englishman Matt Wallace won the title, his third of the year on the European Tour, after prevailing in a four-man playoff with Ryder Cup vice-captain Lee Westwood, Jonathan Thompson and Steven Brown who all finished on 19 under.
Wallace birdied the second playoff hole to claim the title and push himself into contention for one of the four wildcard picks to be announced by Ryder Cup captain Thomas Bjorn on Wednesday.
"I've stepped up to the mark and I've shown him exactly what I'm about," Wallace said.
"If he doesn't pick me, then that's absolutely fine but if he does, he knows he's going to get exactly that in his team."
Sweden's Johan Edfors was the only player to win three times in a Ryder Cup year and not make the team, in 2006.
British Open champion Francesco Molinari, Olympic gold medallist Justin Rose, Tyrrell Hatton and the 2017 Race to Dubai champion Tommy Fleetwood all qualified for the 42nd Ryder Cup via the European Points list.
Olesen claimed his place via the World Points List alongside world number five Jon Rahm, four-times major winner Rory McIlroy and 10-times European Tour winner Alex Noren of Sweden.
The Ryder Cup against the United States takes place in Paris from Sept. 28-30.
(Reporting by Martyn Herman, editing by Pritha Sarkar and Ed Osmond)
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