Singh becomes the 12th person to be ranked No. 1. He joins Woods, Bernhard Langer, Seve Ballesteros, Greg Norman, Nick Faldo, Ian Woosnam, Fred Couples, Nick Price, Tom Lehman, Ernie Els and David Duval as those who have topped the rankings.
Woods has been atop the rankings for a total of 334 weeks.
Ernie Els remains the third ranked player behind Singh and Woods. Masters Champion Phil Mickelson stayed put in the fourth spot, followed by Davis Love III, Retief Goosen, Mike Weir and Padraig Harrington.
Adam Scott, who tied for Woods for second along with Woods at the Deutsche Bank, climbs three spots to ninth. Jim Furyk slipped one spot to 10th.
Sergio Garcia and Stewart Cink exchanged positions from a week ago, with Garcia coming in at No. 11 and Cink 12th. Stuart Appleby and Kenny Perry remained in the 13th and 14th positions, respectively.
Chad Campbell and Darren Clarke flip-flopped spots from last week, with Campbell moving into the 15th slot.
The remainder of the top 20 stayed the same, with Chris DiMarco, Todd Hamilton, Stephen Ames and Scott Verplank in the 17th through 20th positions.
Luke Donald won the Omega European Masters, his second win in five weeks on the European Tour. He jumped from 47th to 35th in this week's rankings.
Duval was the last player other than Woods to hold the top spot in the rankings. Duval played well at the Deutsche Bank, where he tied for 13th. This was the first cut made by Duval since the Capital Open in June 2003. With that finish, Duval jumped from 631st in the world to No. 451 this week.