Europe's Ryder Cup talisman Ian Poulter received a wildcard to make his sixth appearance in the biennial competition against the United States in Paris later this month.
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The quartet join the eight players who qualified automatically for Bjorn's team -- Tommy Fleetwood, Tyrrell Hatton, Rory McIlroy, Francesco Molinari, Alex Noren, Thorbjorn Olesen, Jon Rahm and Justin Rose.
"These four bring so much to the Ryder Cup -- loads of experience, loads of appearances, loads of points won and they know what it's like to win and lose and they'll come in with so much heart and soul," said Denmark's Bjorn as he announced his picks.
He added: "We know what we're up against, we know what the US will bring but I'm confident we can do a good job."
Europe has won six of the last eight Ryder Cups, but USA is the defending champion after victory at Hazeltine in 2016.
The US has not won a Ryder Cup on European soil since Tom Watson's team triumphed at The Belfry in England in 1993.
The 42-year-old Poulter has played on four winning Ryder Cup teams and was a vice-captain two years ago after his season was curtailed by injury.
Poulter's Ryder Cup exploits have earned him the nickname "The Postman" -- because "the postman always delivers" -- and his inspired play at Medinah in Chicago in 2012 set in train Europe's remarkable comeback victory.
Poulter birdied his closing five holes in the Saturday afternoon's final fourball match alongside Rory McIlroy to earn Europe a vital point and drag it back to 10-6 down heading into the Sunday singles.
Europe's subsequent triumph became known as the "Miracle at Medinah."
Poulter, who has won 12 of his 18 matches and halved two, has been in good form this season with a victory on the PGA Tour in Houston and three other top-10 finishes.
"This feels extra special to be part of another Ryder Cup team," Poulter told Sky Sports.
"For Thomas to give me the call means absolutely everything to me. It's going to be an incredible spectacle, it's going to be an extra-strong US team but when you look at the European team on paper I'm getting goosebumps. I can't wait."
Garcia will make his ninth appearance despite a disappointing season in which he missed the cut in all four majors. The 38-year-old, who won the Masters for his first major title in 2017, earned his spot on the back of an impressive Ryder Cup pedigree.
"The one thing about Sergio is he is the heartbeat of the team," Bjorn told Sky.
"It's like a football team going without their captain. Not only is he a fantastic golfer but what he also brings is that he makes everybody around him better. He is what the European Ryder Cup is all about."
Casey, 41, will make his fourth appearance but first since 2008 after recommitting himself to playing sufficient events on the European Tour to be eligible, while former Open champion Stenson will also be playing in his fourth Ryder Cup.
"I've put a lot into this, it's tough to explain," Casey told Sky. "It's an amazing team and I'm very honored. I'm so excited."
On Tuesday, US captain Jim Furyk named Tiger Woods, Phil Mickelson and Bryson DeChambeau as three of his four wildcards for the French showdown.
Already qualified for the US team were Rickie Fowler, Dustin Johnson, Brooks Koepka, Patrick Reed, Webb Simpson, Jordan Spieth, Justin Thomas and Bubba Watson.
Furyk will name his final wildcard Monday. A number of players, including Tony Finau, Kevin Kisner and Xander Schauffele, are in the running.
Europe has five rookies on its team -- Fleetwood, Hatton, Noren, Olesen, and Rahm -- compared with two, former world No.1 Thomas and DeChambeau, so far for the USA.
The Ryder Cup is set to begin at Le Golf National in France on September 28.