Thomas Pieters needed to defend his Czech Masters title and Shane Lowry required a top-four finish in the Wyndham Championship to keep their hopes alive heading into the final qualifying event in Denmark.
However, Pieters lost out by a single shot to American Paul Peterson on Sunday and Lowry was certain to finish down the field in North Carolina after a closing 67.
And that means Yorkshire’s Danny Willett and Matt Fitzpatrick, along with Rory McIlroy, Henrik Stenson, Chris Wood, Sergio Garcia, Justin Rose, Rafael Cabrera-Bello and Andy Sullivan are guaranteed to be on the plane to Minnesota in search of an unprecedented fourth straight win in the biennial event.
Willett, Wood, Cabrera-Bello, Sullivan and Fitzpatrick are the rookies, although Willett won the Masters in April and Wood claimed the BMW PGA Championship at Wentworth in May.
European captain Darren Clarke will name his three wild cards on August 30, with Lee Westwood and Martin Kaymer strong favourites to be selected as Clarke has stressed he would favour experience for a contest on American soil.
Scotland’s Russell Knox and Pieters are understood to be the leading contenders for the final place.
Fitzpatrick has been in the qualifying places ever since winning his maiden European Tour title in the British Masters last October, the 21-year-old then claiming the Nordea Masters in June before a worrying dip in form.
“It’s very exciting now,” Fitzpatrick said after finishing fifth in Prague. “We can look forward to it and get my game in shape.
“I’ve probably been in the team for the longest period of time. It (the qualifying period) started a few weeks before I won at the British Masters and jumped into the team and I’ve managed to stay there since then. It’s been absolutely phenomenal and I’m just delighted to be in the team.
“It’s a great opportunity, I’ve got my first one coming up and hopefully I can just keep pushing on my game and getting better.”
In Prague, it was Paul Peterson secured his first European Tour victory by seeing off defending champion Pieters to claim the title.
America’s Peterson trailed Pieters by two shots heading into the final round, but followed his course-record 64 on Saturday with 67, to close on 15 under par and edge out Pieters by one stroke.
Belgium’s Pieters came agonisingly close to defending his title, losing the lead he had held overnight with just two holes to play.
Pieters jetted 6,000 miles from Rio after finishing fourth at the Olympics in a bid to chase automatic qualification for September’s Ryder Cup.
Back-to-back victories would have proved sufficient to ink his name onto Europe’s team sheet, but now that chance has gone.
Elsewhere, overnight leader Kim Si-woo extended his lead at the Wyndham Championship in North Carolina to four shots on Saturday after following up his brilliant round of 60 with another impressive six-under 64.
The South Korean shot seven birdies, including one at the last, and one bogey to close on 18-under, four strokes clear of nearest challenger Rafa Cabrera Bello from Spain, who posted a five-under score of 65 to finish the third day’s play on 14-under in Greensboro.