The trio will tee-off at 0904 local time at Royal Liverpool Golf Club, the R&A (Royal and Ancient) organisers said on Monday.
Woods, who is now down at number seven in the rankings, is making only his second competitive outing since undergoing back surgery in March.
The 38-year-old American, the game's leading drawcard, missed the cut on his comeback in the Quicken Loans National event in Maryland at the end of last month.
Woods has won 14 majors in his career and lifted the coveted Claret Jug when the British Open was last played at Hoylake in 2006.
World number one Adam Scott launches his campaign at 1427 on Thursday alongside last week's Scottish Open winner Justin Rose and U.S. PGA champion Jason Dufner.
Title holder Phil Mickelson goes out at 1405 with 2002 and 2012 winner Ernie Els and U.S. Masters champion Bubba Watson.
Mickelson believes Englishman Rose, the world number three, has a good chance of repeating the American's feat 12 months ago when the popular left-hander followed up his Scottish Open victory by winning the third major of the season.
"It's an advantage to play the Scottish Open on a links course ... get acclimatised to seeing the ball bounce, the fescue and thicker grasses on the greens and the long lag putts that we are going to have here," said the five-times major winner.
"The fact that he is playing well means he is going to be incontention. It worked for me - I thought winning the Scottish was very instrumental in propelling me to The Open."
World number eight Rory McIlroy starts out at 0926 local time in the company of rising young American Jordan Spieth and Japan's Hideki Matsuyama.
England's David Howell, in a three-ball with 2001 Open champion David Duval and former European number one Robert Karlsson of Sweden, will have the honour of hitting the first shot of the championship at 0625.
(Editing by Alan Baldwin)
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