Woods won the last two Open Championships at St. Andrews in 2005 and last year at Royal Liverpool. Lawrie won the last Open played at Carnoustie in 1999.
Rose, playing as an amateur, was the darling of the 1998 British Open at Royal Birkdale, where he shared fourth place behind playoff winner Mark O'Meara.
That threesome will tee off Thursday morning at 9:09 a.m. local time, which is 4:09 a.m. ET. They then tee off Friday at 9:20 a.m. ET.
American Joe Durant will hit the first tee shot Thursday at 6:30 a.m. local time.
Another featured group includes last year's runner-up Chris DiMarco, paired with five-time European Ryder Cupper Darren Clarke and 2005 U.S. Open winner Michael Campbell. They play at 7:58 a.m. local time Thursday and 1:09 p.m. Friday.
Two-time U.S. Open winner Retief Goosen tees off Thursday morning at 8:09 a.m. local time with 1997 British Open champ Justin Leonard and two-time Open runner-up Thomas Bjorn.
That threesome will be followed by 2006 U.S. Open winner Geoff Ogilvy, 2004 British Open champ Todd Hamilton and Anthony Wall.
Three-time British Open winner and 11-time European Ryder Cup performer Nick Faldo will be joined by Carl Pettersson and Trevor Immelman on the first tee at 8:42 a.m. local time Thursday.
Eight-time European Order of Merit winner Colin Montgomerie is paired with Toshi Izawa and Stewart Cink at 9:31 a.m. local time Thursday.
Tom Lehman, the 1996 British Open champion, plays with Jeev Milkha Singh and Nick O'Hern in the following group.
Ernie Els, the 2002 Open winner, is joined by Robert Karlsson and Lucas Glover the first two days. They will be followed by Robert Allenby, Bradley Dredge and 1995 British Open victor John Daly.
Newly crowned U.S. Open winner Angel Cabrera tees off at 1:09 p.m. local time Thursday with Rory Sabbatini and 2005 PGA TOUR Rookie of the Year Sean O'Hair. The following group will be Padraig Harrington, 2001 U.S. PGA Championship winner David Toms and reigning U.S. Amateur champion Richie Ramsay.
World No. 2 Phil Mickelson, who is coming off a tough loss at the Scottish Open, tees off Thursday at 2:20 p.m. local time with Toru Taniguchi and five-time European Ryder Cupper Lee Westwood. They come back at 9:09 a.m. Friday.
Zach Johnson, who won The Masters in April, is paired with Graeme McDowell and Spaniard Jose Maria Olazabal. They tee off at 2:31 p.m. local time Thursday and are followed by Chad Campbell, Sergio Garcia and Johan Edfors.
He was elected to the World Golf Hall of Fame in 1999.