United States Ryder Cup captain Tom Watson praised Tiger Woods for taking the "high road" by ruling himself out of next month's contest at Gleneagles.
Woods, 38, has been suffering from a persistent back problem and had failed to qualify for the US team automatically.
Nevertheless, Watson was considering Woods as one of his captain's picks.
"My primary wish is for Tiger to be healthy and competitive," said Watson. "I hope that he'll return very soon."
Woods had surgery on his back injury in March and has been told not to play by doctors after aggravating the problem at the recent WGC-Bridgestone Invitational in Ohio.
He said he was pain-free at the US PGA Championship a few days later but re-injured himself before his second round and went on to miss the halfway cut for just the fourth time in 66 majors as a professional.
"Of course, I'm disappointed that Woods has asked not to be considered for the US Ryder Cup Team, and that his health is not where he would like it to be," added Watson.
"However, I think we can all agree that we need Woods in this great sport, and he has taken the high road by informing me early on in the selection process."
|Tiger's 2014 in numbers (PGA Tour)|
|Best finish||Tied 25th (WGC-Cadillac Championship)|
|Times missed cut||Twice|
|Year-to-date earnings||£65,000 ($108,275)|
|Current world ranking||11th|
"My focus will remain on identifying three players to join the US team and give us the best chance for success at Gleneagles," he added.
Former Ryder Cup player Andrew Coltart believes Watson will be relieved by Woods' decision.
"I don't think necessarily it's going to be a bad thing for the US team," said Coltart, who lost to Woods in the singles at Brookline in 1999, the only time the 14-time major winner has been on a winning team.
"Certainly it's a bit of a relief for Tom Watson because it was a huge decision that he was going to have to come up with. The decision has been made for him."
|Tiger's Ryder Cup record|
|Participations||Seven (1997, 1999, 2002, 2004, 2006, 2010, 2012)|
|Record||Won 13, Lost 17, Halved 3|
|Total points won||14.5|
He added on Sky Sports: "Watson getting the freedom to pick somebody else, I think will possibly make that American team a little stronger."
Europe will go into the tournament in Perthshire, Scotland, which takes place between 23-28 September, as the holders.
Jose Maria Olazabal's team beat the United States 14.5-13.5 at the Medinah Country Club in Illinois in 2012.