Weir, who won a playoff last year with Len Mattiace, will begin his opening round at 1:19 p.m. (ET) and will play in a threesome with Justin Leonard and U.S. Amateur champion Nick Flanagan. The same group will start play Friday morning at 10:23 a.m.
Woods, who won in 1997 and again in '01 and '02, will start Thursday and Friday in the group directly after Weir. Woods' playing partners include Thomas Bjorn and U.S. Amateur runner-up Casey Wittenberg.
This year's field of 93 includes 17 first-time players. The first round gets underway Thursday morning at 8:00 a.m.
Perennial contender Phil Mickelson, still trying for that elusive first major title, will play the first two days in a group with international stars Darren Clarke and Shigeki Maruyama.
Ernie Els, who has also come close to winning the coveted Green Jacket, will play with 1998 winner Mark O'Meara and Robert Allenby, while 2000 champion Vijay Singh will tee it up with Padraig Harrington and John Daly.
Two-time Masters runner-up Davis Love III will join former U.S. Open champ Retief Goosen and two-time Masters winner Jose Maria Olazabal.
A group of former Masters winners features Gary Player, Ben Crenshaw and Larry Mize, while six-time champion Jack Nicklaus will join international players Alex Cejka and Toshi Izawa.
Arnold Palmer, the four-time champion playing in his 50th Masters, will start with Bob Estes and mid-Amateur champion Nathan Smith.