Woods has won three U.S. Opens, including a record 15-stroke triumph at Pebble Beach in 2000.
Rose was the 2013 champion at Merion, while Spieth triumphed two years later at Chambers Bay.
Two groups ahead of Woods, Spieth and Rose, two-times defending U.S. Open champion Brooks Koepka will play with Italian Francesco Molinari and amateur Viktor Hovland.
Norwegian Hovland won last year's U.S. Amateur Championship at Pebble Beach.
Early-arriving fans next Thursday will have no shortage of choice for big names to watch.
Northern Irishman Rory McIlroy starts his quest to end his five-year major drought at 7.51 a.m., teeing off at the 10th hole with Spaniard Jon Rahm and Australian Marc Leishman.
Two groups later, Graeme McDowell, the 2010 U.S. Open champion at Pebble Beach, will play with 2016 champion Dustin Johnson and six-times runner-up Phil Mickelson, who needs a victory to complete the career grand slam.
Tee times are switched for the second round, so those who play early on Thursday go out late on Friday, and vice-versa.
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond)
