Finau was the final wildcard pick for USA Ryder Cup captain Jim Furyk and was only announced on Monday after the BMW Championship.
Finau finished tied eighth with Xander Schauffele in tied third another contender for the slot.
Schauffele led after day two and appeared to be putting late pressure on Finau.
But the 28-year-old got the nod having registered eight top-10s through the regular season and now another three in the first three FedExCup play-off events.
I’ve still got goosebumps,” Finau said.
“I’m just ecstatic. I don’t know if I can really put it into words. All the emotions that come with accomplishing something like that… man, it’s a dream come true for me.
“I got the goosebumps when he [Furyk] told me, and I’m excited to add my skills and talent to the team – a team that’s stacked already. Hopefully I bring something to the team that can help us bring that cup back.”
And he tweeted: “A dream come true!! Incredibly honored to be a part of @RyderCupUSA!
“Excited to join the team and do whatever it takes to help us bring home a victory!!
“Thanks to Captain Jim Furyk for believing in me and to all the fans for their support. I’m truly humbled.”
The American side is now made up of Dustin Johnson, Brooks Koepka, Patrick Reed, Webb Simpson, Justin Thomas, Bubba Watson, Jordan Spieth, Rickie Fowler, Tiger Woods, Phil Mickelson and Bryson DeChambeau.
They will face a European side consisting of Paul Casey, Tommy Fleetwood, Sergio Garcia, Tyrell Hatton, Rory McIlroy, Francesco Molinari, Alex Noren, Thorbjorn Olesen, Ian Poulter, Jon Rahm, Justin Rose and Henrik Stenson.