Finau had been considered a hot favourite based on his strong recent form.
The 28-year-old has not won on the PGA Tour, but had top-10s at three majors this year, and has played well during the current FedExCup playoffs.
The long-hitting world number 17 will be one of three rookies on the American team, along with Bryson DeChambeau and Justin Thomas.
"He has an unbelievable body of work this year," said Furyk.
"All those top-10 finishes, the play in big championships and the majors, and then his current form, a second, a fourth and an eighth in the playoffs. He checked a lot of boxes and made it impossible not to pick him."
Finau said he was thrilled to join a Ryder Cup team that includes nine major champions.
"It’s a dream come true for me," said Finau. "I got the goosebumps when he told me, and I'm excited to add my skills and talent to the team, a team that's stacked already," he said.
"Hopefully I bring something to the team that can help us bring that Cup back."
U.S. TEAM
Brooks Koepka
Dustin Johnson
Justin Thomas
Patrick Reed
Bubba Watson
Jordan Spieth
Rickie Fowler
Webb Simpson
Tiger Woods
Phil Mickelson
Bryson DeChambeau
Tony Finau
(Reporting by Andrew Both; Additional reporting by Rory Carroll; Editing by Ken Ferris)
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