Bjørn became the first Danish Ryder Cup player in history in 1997, before appearing in the biennial contest twice more in 2002 and 2014 – experiencing victory on all three occasions. In 2018 he was European Ryder Cup Captain and led Team Europe to a 17.5 – 10.5 win at Le Golf National, Paris.

Bjørn won his first Legends Tour title at the 2021 Irish Legends presented by the McGinley Foundation, defeating 2002 Ryder Cup teammate Phillip Price in a play-off.
 
Bjørn started his career on the Challenge Tour, winning four titles on his way to topping the Rankings in 1995, and remains a strong supporter of the developmental tour. He became the first graduate to captain a Ryder Cup team.