The 38-year-old failed to qualify for the team outright and has now informed the PGA of America and Ryder Cup captain Tom Watson that, after playing just four tournaments on his return to action following back surgery, he does not wish to be considered for one of the three remaining places.
Woods has struggled with personal problems and a series of injuries since winning his most recent major championship at the 2008 US Open, with a back injury the latest to disturb his career.
Woods underwent back surgery on March 31 and has now admitted he will not be fit to participate at Gleneagles.
"While I greatly appreciate Tom thinking about me for a possible captain's pick, I must take myself out of consideration," Woods said in a statement on www.pga.com.
"I've been told by my doctors and trainer that my back muscles need to be rehabilitated and healed. They've advised me not to play or practice now.
"I'm extremely disappointed that I won't be ready for the competition.
"The U.S. Team and the Ryder Cup mean too much to me not to be able to give it my best. I'll be cheering for the U.S. Team. I think we have an outstanding squad going into the matches."
After his surgery, Woods did not return to action until the end of June, missing the cut in the Quicken Loans National and then finishing 69th in the Open at Royal Liverpool, his worst 72-hole finish in a major in the paid ranks.
He withdrew after hitting his tee shot on the ninth hole of his final round at the WGC-Bridgestone Invitational 11 days ago and was a major doubt to even take part in the US PGA Championship last week.
The 14-time major winner missed just his fourth cut in 66 majors as a professional after suffering yet more back trouble at Valhalla but Watson insisted he was still in his thoughts and that he trusted Woods to be honest about his physical condition.
And the captain now knows Woods will not be an option when he makes his three picks on September 2.
"My primary wish is for Tiger to be healthy and competitive, and I hope that he'll return to the game very soon," said Watson.
"Of course, I'm disappointed that Tiger Woods has asked not to be considered for the U.S. Ryder Cup Team, and that his health is not where he would like it to be.
"However, I think we can all agree that we need Tiger Woods in this great sport, and he has taken the high road by informing me early on in the selection process.
"My focus will remain on identifying three players to join the U.S. team and give us the best chance for success at Gleneagles."
Woods would not have been a certainty for a pick even if he had been fit with Watson also admitting that form would have to play a major part in any decision.
Barring the USA win at Valhalla in 2008 when Woods was recovering from knee surgery, he had played in every Ryder Cup since 1997, winning at Brookline in 1999, and had a record of 13 wins, 17 losses and three halves.
Bubba Watson, Rickie Fowler, Jim Furyk, Jimmy Walker, Matt Kuchar, Jordan Spieth, Patrick Reed, Zach Johnson and Phil Mickelson are the nine automatic qualifiers for a place on the 12-man American team.
Keegan Bradley looks to be the most likely candidate for a wild card given his three wins from three matches with Phil Mickelson at Medinah in 2012, but Watson has injury concerns over Kuchar and prospective pick Jason Dufner.
Kuchar withdrew from the US PGA before the start with back spasms, while Dufner's title defence lasted just 10 holes with a long-standing neck problem and he dropped out of the qualifying places.