Woods, whose two British Open crowns have come at St. Andrews, will be playing for just the third time since the Masters and the death of his father, Earl, earlier this spring.
Faldo and Woods will be joined in their group by Japan's Shingo Katayama when they tee off Thursday at 9:09 a.m. (et).
There are some stellar groups in the early session on Thursday. Former Masters champion Fred Couples is paired with Paul Casey and Sergio Garcia. They will tee off at 2:36 a.m. (et) Thursday. Another former Masters winner, Mike Weir, headlines the following group.
Ernie Els, the 2002 Open champion, will play with Luke Donald and U.S. Amateur champion Edoardo Molinari at 2:58 a.m. Former U.S. Open winner Jim Furyk will follow Els and is grouped with Rod Pampling and Greg Owen.
Two-time major winner Vijay Singh is paired with Zach Johnson and European Tour Order of Merit leader David Howell in the group behind Furyk at 3:20 a.m.
Eight-time Order of Merit winner Colin Montgomerie, who finished second to Woods at St. Andrews last year, is grouped with Stuart Appleby and former Open champion John Daly.
Two groups later, reigning Masters and PGA champion Phil Mickelson will play with Yasuharu Imano and Darren Clarke.
Newly crowned U.S. Open champion Geoff Ogilvy will be joined on the first tee at 8:20 a.m. Thursday by Carl Pettersson and Chris DiMarco. Two groups later, world No. 6 Adam Scott will play with British Amateur winner Julien Guerrier and world No. 13 Henrik Stenson.
Following Woods' group will be Hideto Tanihara, Paul McGinley and David Duval. Duval, who is having a solid season, is still looking for his first win since claiming the 2001 British Open at Royal Lytham & St. Annes.
World No. 4 Retief Goosen, a two-time U.S. Open winner, tees off three groups after Woods on Thursday at 9:42 a.m. Goosen will play with reigning European Tour Rookie of the Year Gonzalo Fernandez-Castano and five-time British Open champion Tom Watson, who claimed his second Senior British Open crown last year.