Furyk, who was the losing Ryder Cup captain at Paris in 2018, succeeds Keegan Bradley in the role after the latter found himself in the crosshairs last September at Long Island's Bethpage Black over a series of questionable line-up decisions.
The 55-year-old Furyk joins Jack Nicklaus, Tom Watson and Davis Love III as the only US Ryder Cup captains to receive a second term in the era of European continental inclusion.
"The opportunity to captain the US Ryder Cup Team for a second time is a tremendous honour. I am committed to putting our players in the best position to succeed as we work to reclaim the Cup on European soil," said Furyk.
At the 2018 Ryder Cup, Furyk became the sixth consecutive American leader to preside over a losing team in Europe.
After the blowout seven-point loss, Furyk faced tough questions about what he could have done differently, including whether it was negligent that half his team arrived at quirky Le Golf National without having stepped foot on the course.
Furyk also served as the winning US captain at the 2024 Presidents Cup in Montreal.
Woods had been the favourite to assume the Ryder Cup captain's position but the PGA of America announced in early April that he declined to take the role as he stepped away to seek treatment and focus on his health after his arrest on a DUI charge stemming from a rollover crash in Florida.
The 15-times major champion has been a long-time presence in team events, including serving as a player-captain at the 2019 Presidents Cup.
Luke Donald was named European captain for a third consecutive Ryder Cup in March as he aims to become the first captain to guide a team to three-straight victories next year.
The 2027 Ryder Cup will be held September 17-19.
