The 45-year-old will be the first man from Scandinavia to lead Europe in golf's most prestigious team event, which will be held in France for the first time.
He was on the winning side in three appearances as a player, in 1997, 2002, and 2014, and was a non-playing vice-captain on four occasions -- including October's 17-11 defeat at Hazeltine under Darren Clarke that ended Europe's eight-year reign.
With 15 European Tour titles since his rookie year in 1996, Bjorn is Denmark's most successful golfer, and was the first from his country to play in the Ryder Cup.
"This is one of the greatest days in my career," Bjorn said
after being given the captain's role by a five-man panel ahead of fellow 2016 deputy Paul Lawrie of Scotland.
"I have lived and breathed the European Tour for so long, and now I will do the same with the Ryder Cup for the next two years. I'm very much looking forward to taking on this task.
"I studied a lot of captains as a player and as a vice-captain and always wondered what that feeling would be like to be the one leading out a team of 12 great players.
"Now it's my turn to do just that and it is an exciting moment for me."
The selection panel comprised Clarke, his predecessors Paul McGinley and Jose Maria Olazábal, European Tour chief executive Keith Pelley
and Race to Dubai winner Henrik Stenson
, also a member of the circuit's tournament committee.
Pelley said Bjorn was picked for his experience, commitment and passion.
"He wants the Ryder Cup to be the greatest sporting event it can be. So when you look at these characteristics, I am convinced they will make him a great Ryder Cup captain," the Canadian said.
Europe had won six of the last seven Ryder Cups before being crushed by Davis Love's team in Minnesota.
The 2018 edition will be held at Le Golf National in Saint-Quentin-en-Yvelines, 25 km from central Paris. It will be only the second time the tournament has been staged in Continental Europe.