The 18-hole contests, starting in January 2024, will take just two hours to complete.
Homa has made no secret of his admiration for Woods.
The 46-year-old insists he has no intention of retiring though and still plans to play in the Open again.
Woods miss the cut in the Open for just the fourth time in his career.
Dustin Johnson set the early clubhouse target after a second-round 67.
The 15-time major winner never recovered from a nightmare start.
Two of the 46-year-old’s three Claret Jugs have been won on the Old Course, in 2000 and 2005.
The 15-time major winner said he could not understand why leading players have “turned their backs” on the PGA Tour.
Nick Faldo, John Daly, Louis Oosthuizen and Zach Johnson teamed up to shoot six under par.
The 15-time major winner was again accompanied by US PGA champion Justin Thomas.
