They join Bryson DeChambeau, the hottest player in golf, as three of the American wild-card selections.
U.S. captain Jim Furyk had an easy time with three of his four picks. DeChambeau, Mickelson and Woods were the next three in the U.S. standings behind the eight players who earned automatic spots after the PGA Championship.
DeChambeau has won the last two FedEx Cup playoff events, rising to No. 7 in the world.
Still to come for Furyk is his final captain’s pick, to be announced Monday after the BMW Championship.
The matches are Sept. 28-30 outside Paris.