Having claimed a third victory in his last 15 tournaments, Wallace could now be a contender, alongside Fitzpatrick, for one of Bjorn's four wild-card picks, which the Dane will reveal on Wednesday.
Despite finishing 8 shots off the lead at his home tournament, Olesen can now watch Bjorn's announcement over the Sept. 28-30 matchup with the United States at Le Golf National in Paris with his place assured.
"Relief is my first emotion, that's for sure," Olesen said. "It's been a tough week, a long week."
Fitzpatrick came up short but will hope his 6-under 66 to end the tournament 16 under will have impressed Bjorn.
Another Englishman, Eddie Pepperell, also could have snatched the final qualification spot from Olesen if he had won the tournament but wasn't in contention going into the final round, eventually finishing 14 shots off the pace.
"I want to congratulate the eight players who have automatically qualified for The 2018 Ryder Cup team," Bjorn said. "They have all played some incredible golf to make it, and every single one of them is a world-class golfer who will represent Europe with pride and commitment."
Olesen is one of five players -- along with Rahm, Noren, Hatton and Fleetwood -- who will make their Ryder Cup debuts.
Bjorn has a difficult decision ahead for his four at-large picks. Among the players he has to choose from will be veterans Ian Poulter, Henrik Stenson, Paul Casey and Sergio Garcia, along with Rafael Cabrera Bello, Thomas Pieters, Fitzpatrick and Matt Wallace -- whose victory on Sunday in Denmark was his third win on the European Tour this year.
U.S. captain Jim Furyk announces the first three of his four wild-card picks on Tuesday.
ESPN's Bob Harig and The Associated Press contributed to this report.