Scott, 33, is the first Australian to be world number one since his boyhood hero Greg Norman, who spent 331 weeks in the position in the 1980s and '90s.
The 2013 Masters champion was inactive last week, but was already assured of taking top spot with Woods sidelined with a long-standing back problem.
Playing in the Byron Nelson Championship, American Matt Kuchar could also have moved ahead of Woods, but tied for seventh and had to settle for fourth spot in the rankings.
Woods returned to the top of the world rankings in March, 2013, taking over from Rory McIlory and he has been there ever since.
The American has spent a total of 683 weeks as the world's best during the course of his career.
Scott becomes the 17th player to become world number one since Germany's Bernhard Langer was the first in 1986.
"The ranking system is just the way it is," Scott said of the two-year revolving points system that makes his ascension possible. "It's a very hard system to perfect with tours all over the world.
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