Bradley succeeds twice major champion Zach Johnson as US captain after the latter faced plenty of criticism following the last edition of the biennial event where his squad failed to get the job done against Europe.
"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," PGA of America President John Lindert said in a news release.
Woods, who won the 2002 US Open at Bethpage Black, had been the overwhelming favourite to take over as captain but has been busy off the golf course and previously said he was unsure if he could devote the necessary time the position demands.
For Bradley, who counts the 2011 PGA Championship among his six wins on the PGA Tour, his appointment as captain comes after he was left off the 2023 US Ryder Cup squad in a year in which his six top-10 finishes on the PGA Tour included two wins.
In his two Ryder Cup appearances - 2012 and 2014 - Bradley amassed a 4-3 record.
"My passion and appreciation for golf’s greatest team event have never been stronger," said Bradley.
"The Ryder Cup is unlike any other competition in our sport, and this edition will undoubtedly be particularly special given the rich history and enthusiastic spectators at this iconic course. I look forward to beginning preparations for 2025."
While Woods discussed the captaincy with the PGA of America he is, in addition to playing a limited schedule, also involved in numerous business ventures and part of the peace negotiations between the PGA Tour and Saudi backers of LIV Golf.
When asked about the captain's job in May ahead of the PGA Championship, Woods said the two sides were still talking about what that would look like and whether he had the time to do it.
"I'm dedicating my so much time to what we're doing with the PGA Tour, I don't want to not fulfil the role of the captaincy if I can't do it," Woods said in May.
"What that all entails and representing Team USA and the commitments to the PGA of America, the players, and the fans and as I said, all of Team USA. I need to feel that I can give the amount of time that it deserves."
The 15-times major champion was an obvious candidate for the captaincy having made eight appearances as a player in the Ryder Cup between 1997 and 2018 during which he compiled an overall record of 13-21-3.
Woods was also a victorious player-captain for the 2019 Presidents Cup in Melbourne and has served as a captain's assistant in both that event and the Ryder Cup.
Team Europe announced last November that Luke Donald, who led his team to a convincing Ryder Cup victory in Italy last year, will return as captain for the 2025 edition.
