Scott, who spent the past 38 weeks as the second ranked player, has had chances to overtake Woods through high tournament finishes but has instead done so with both players out of action.
The updated rankings are released on Monday.
Woods last played in March and is out indefinitely following back surgery, making his fall from the top inevitable.
The 33-year-old Scott is just the second Australian to reach the top ranking, following Greg Norman's final reign which ended in 1998.
"This is another outstanding achievement for Adam Scott," Brian Thorburn, Chief Executive of the PGA of Australia, said in a statement.
"The Australian golfing community is very proud of Adam and we look forward to watching his progress throughout the year."
The 2013 Masters champion, Scott, ends Woods' stretch of 60 straight weeks at the top.
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