Bjorn, 45, succeeds Northern Irishman Darren Clarke. He was vice-captain for four previous Ryder Cups, including this year's 17-11 loss to the United States at Hazeltine.
"It's a huge honour for me to be named European captain for the 2018 Ryder Cup in Paris," Bjorn said in a statement on the Ryder Cup website. "This is one of the greatest days in my career."
Bjorn, who is Denmark's most successful golfer, has played in three Ryder Cups and twice finished second in the British Open.