Tiger Woods and Phil Mickelson, golf's most prominent players for more than two decades, never realized the Ryder Cup would mean so much.

For Woods, it's the culmination of a comeback that began in January after a fourth surgery on his lower back.

For Mickelson, more than setting a record by playing his 12th Ryder Cup, the 48-year-old gets what he believes will be his last chance to capture the gold trophy away from home.

US captain Jim Furyk added Woods and Mickelson to his team as wildcard selections on Monday, along with Bryson DeChambeau.

Woods agreed to be a vice-captain in late February, and he set a goal to be playing in Paris from Sept 28-30.

"It's incredible, it really is, to look back at the start of the year and now to have accomplished a goal like that," Woods said.

"To be a part of this team, and now to be a player is just ... beyond special."

Mickelson had qualified for every team since 1995, a streak that ended this year when he finished No 10 in the standings. His 12th appearance breaks the Ryder Cup record held by Nick Faldo.

Mickelson has only been on three winning teams - at Brookline in 1999, Valhalla in 2008 and two years ago at Hazeltine.

His last time overseas was at Gleneagles, where he memorably closed out a losing news conference by questioning captain Tom Watson and the direction the PGA of America was taking the US team.

That led to sweeping changes in the US structure, mainly by giving players a stronger voice.

"This is mostly likely my last chance to go over to Europe and to be a part of a winning US team; we haven't done that in 25 years," Mickelson said.

"I set out this year on really a strong commitment to get on the team. I got off to a great start and it's been a really good year. Although I fell just shy of making it on points, it feels great to be a part of this team and serve any way I can."

Furyk still has one more captain's pick he will announce after the BMW Championship, and it might not be as easy as this one.

"Not that it was an easy decision," Furyk said. "But it could have been a lot more difficult."

Tony Finau is believed to be the leading candidate for the 12th and final spot. Furyk invited him as part of a small group that played Le Golf National near Paris on the weekend before the British Open. Finau tied a PGA Championship record with 10 birdies in the second round while playing with Furyk.

During the FedEx Cup playoffs, he was runner-up at one event and tied for fourth at the other.