Woods had back surgery before the Masters and missed the opening two majors.
He tees off at 9:04 a.m. GMT at Royal Liverpool.
Defending champion Phil Mickelson is on the other side of the draw, starting Thursday afternoon with Ernie Els and Masters champion Bubba Watson.
Justin Rose, coming off victories in the Scottish Open at Royal Aberdeen and the Quicken Loans National at Congressional, also is in the afternoon side of the draw. Rose has emerged as a favourite to claim the claret jug. He plays with world No. 1 Adam Scott and PGA champion Jason Dufner.