Harrington had earlier indicated that Garcia and Poulter, who play a total of 15 games in the Ryder Cup, should be selected.
Wiesberger, Lee Westwood, Matt Fitzpatrick and Tyrrell Hatton secured the last automatic qualifying places for Europe after the BMW PGA Championship on Sunday. They joined Hovland, Jon Rahm, Rory McIlroy, Tommy Fleetwood and Paul Casey in the team for the September 24-26 event.
Europe will strive to retain the Ryder Cup after defeating the US team in 2018.
The Associated Press contributed to this report.