Finau's place was announced after he finished in a tie for eighth at the BMW Championship in Philadelphia.
The 28-year-old from Salt Lake City - ranked 15th in the world - claimed his only PGA Tour title to date at the 2016 Puerto Rico Open.
"Hey guys, Tony Finau here. I'm so excited to be on the Ryder Cup team and I cannot wait to get to Paris," he said in a short video posted on the Ryder Cup USA Twitter account.
"Thanks for all the support - go USA."
Furyk chose Tiger Woods, Phil Mickelson and Bryson DeChambeau with his first three picks on September 4.
Those four players will join Rickie Fowler, Dustin Johnson, Brooks Koepka, Patrick Reed, Webb Simpson, Justin Thomas, Bubba Watson and Jordan Spieth, who qualified automatically.
The 2018 Ryder Cup will be staged at Le Golf National in Paris, which is hosting the event for the first time.
Team Europe, captained by Thomas Bjorn, contains new world number one Justin Rose, along with Paul Casey, Tommy Fleetwood, Sergio Garcia, Tyrrell Hatton, Rory McIlroy, Francesco Molinari, Alex Noren, Thorbjorn Olesen, Ian Poulter, Jon Rahm and Henrik Stenson.
In the 2016 Ryder Cup, held at Hazeltine National, the United States team won 17-11.
An American team has not won in Europe since the 1993 triumph at The Belfry.
