Bjorn carded a four-under-par 68 in his final round at Penha Longa for a 23-under 265 aggregate, which left him five shots clear of nearest rival Richard Green of Australia (70).
Denmark's Mark Haastrup finished third seven strokes behind Bjorn.
Victory ended four years of frustration when Bjorn was beset by illness and niggling injuries as well as loss of form.
"I knew it would come back one day and it is made better knowing I played well all week," he told Reuters.
"I'm very pleased I held it together with Richard coming at me strongly, the saves for par were very important, all in all a satisfying day."
Bjorn's success, though, will only earn him one year's automatic exemption for next season.
Last year, the European Tour's players' committee, with Bjorn as chairman, decided to halve the exemption for all tournaments with prize funds of less than 1.5 million euro. This event had a purse of one million euro.
Strong breezes made Bjorn work for the $205,000 first prize as the 39-year-old claimed his 10th European Tour title.
Bjorn scrambled valiantly over the front nine as the wind increased speed, holing par-saving putts of 12, nine and seven feet on his way to the turn three ahead, the position he had been overnight.
His save from 12ft came on the eighth after he drove on to a cart-path, sending his ball into the bottom of a portable television camera cart.
A missed birdie putt of only 15 inches by Bjorn on the long 12th could have proved costly as Green moved within just a stroke of him with five holes to play.
However, two-shot swings on the 14th and 15th finally ended Bjorn's barren spell as he birdied both holes to Green's bogeys.
Bjorn's splendid approach to birdie the final hole put the icing on the cake for the Dane.
