Woods had been a long-time favourite to succeed Zach Johnson and lead the US side as they look to bounce back from a 16½-11½ defeat in Rome last September.
But the former world number one, who played on eight Ryder Cup teams, repeatedly delayed his decision.
He said at the US PGA Championship in May that he did not want to “fulfill the role of the captaincy if I can’t do it”, citing his position on the PGA Tour policy board as something that was taking up a lot of his time.
And given the announcement of Bradley as captain, it would appear Woods finally decided he could not dedicate the time to the role that he would want to.
Bradley, who won his solitary major at the 2011 US PGA Championship, was on the losing Ryder Cup teams in 2012 – as Europe won the ‘Miracle of Medinah’ – and two years later at Gleneagles in Scotland.
PGA of America president John Lindert, who made the announcement, said: “Keegan’s past Ryder Cup experience, strong relationships and unwavering passion for this event will prove invaluable as he guides the US team over the next year and a half.
“We are confident that with Keegan at the helm, the 2025 US Ryder Cup Team will compete at Bethpage with the same confidence and determination that has defined his career.”
It would appear to be a change in direction for the PGA of America, who run the US Ryder Cup team.
Recent captains Johnson, Jim Furyk and Davis Love III all served as an assistant captain at least once before taking on the top job.
Bradley, who has won five PGA Tour events, to add to his major, since turning professional in 2008, has not been near the side since 2014.
In his two Ryder Cup appearances, he won four and lost three matches – one of the defeats being in a singles match against Rory McIlroy in 2012 when the Northern Irishman almost missed his tee-time.