Tiger Woods will attempt to win the Memorial Tournament for a sixth time as he continues his preparations for next month's U.S. Open.
Justin Thomas will get the opportunity to assess Le Golf National ahead of the Ryder Cup when he plays in the Open de France.
Webb Simpson reflected on an "incredible week" and said his final-round struggle was a "mystery" after he "hung in there" at Sawgrass.
An 11th-placed finish for Justin Thomas moved him top of the rankings and he plans to hold that status for the long haul.
At one point on Sunday, Tiger Woods looked capable of pulling off a shock victory. "He'll win sometime soon enough," said Jordan Spieth.
American Justin Thomas became the 21st player to reach world number one since the rankings started in 1986.
Webb Simpson captured The Players Championship after entering the final round with a seven-shot lead at TPC Sawgrass on Sunday.
Tiger Woods was among the chasers applying the pressure on Webb Simpson, who led by five shots at the turn.
Koepka shot nine-under (63) during his round Sunday to jump all the way up into a tie for third on The Players Championship leaderboard.
Mike Lorenzo-Vera failed to convert a third-round lead into a first European Tour win, as Joakim Lagergren won the Rocco Forte Open.