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The Dane birdied the first hole of a sudden death play-off to snatch victory away from the 36-year-old after both players tied in the clubhouse at 20-under-par.
Lee pulled on his golf clothing on Sunday two shots clear of Björn, Spaniard Alejandro Cañizares and Frenchman Victor Dubuisson.
However, the Scot soon came under pressure from Björn, who raced to the turn in 31 shots to take the lead at 19-under-par, one ahead of Cañizares and Dubuisson.
Lee rallied on the back nine with birdies at 12, 14 and 15 to draw level with Björn, who also carded a birdie at 15, on 20-under-par.
The Scot had a chance to win the tournament outright on 18, but his birdie attempt burned the hole, meaning that the pair were forced back down the last.
This time it was the Dane who had the opportunity to take the title with a 12-foot birdie putt, which he stroked home.
It marked a stellar display from the 43-year-old, who made only two bogeys over the course of the week, including a flawless final round 65 on Sunday.
Björn's victory puts him to the top of the European Ryder Cup points ranking, as the Dane looks to stake his claim for a third Ryder Cup appearance.
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