Updated

New York, NY (SportsNetwork.com) - United States captain Tom Watson tabbed veterans Keegan Bradley, Hunter Mahan and Webb Simpson on Tuesday to round out his Ryder Cup team.

Bradley and Simpson played in the 2012 Ryder Cup, and followed up by playing in last year's Presidents Cup. Mahan played in the 2008 and 2010 Ryder Cups and has played the last four Presidents Cups for the United States.

"I've had the opportunity to meet and be with a lot of players over the last two years. The process has been getting to know them and get to know how they feel about the Ryder Cup, and I can tell you everyone of them wanted to make amends for Medinah," said Watson of the 2012 Ryder Cup, where the Europeans rallied to victory.

Those three join Bubba Watson, Rickie Fowler, Jim Furyk, Jimmy Walker, Phil Mickelson, Matt Kuchar, Jordan Spieth, Patrick Reed and Zach Johnson, who were the nine qualifiers for the U.S. team.

Bradley has played on the last two international teams for the United States, at the 2012 Ryder Cup and the 2013 Presidents Cup. He went 3-1 in his first Ryder Cup and teamed with Phil Mickelson in his three victories, but Bradley lost to Rory McIlroy in their singles match. Bradley was 2-2-1 at the Presidents Cup, with a 2-1-1 mark when paired with Mickelson.

The 2011 PGA Champion hasn't won since the 2012 season, but Bradley was the runner-up at the Arnold Palmer Invitational and has three fourth-place finishes, including at the U.S. Open and the WGC-Bridgestone Invitational in 2014.

"I've made no secret of how important this team is to me and how bad I want to go back and win the Ryder Cup. This is a redemption year for a lot of the guys that were on the team last time. It's just going to be an unbelievable trip over to Scotland," Bradley stated. "I'm not going to hide my emotion. I think the Ryder Cup is a time to let the emotion come out of you. The Ryder Cup is a great example of when you can let (the emotion) go."

Mahan will be making his third Ryder Cup appearance. He is just 0-1-1 in his previous two singles matches, but is 3-1-2 in foursomes and fourballs combined. Mahan won the Barclays two weeks ago for just his sixth top-10 of the season. Two of those came in World Golf Championship events, and he shared seventh at the PGA Championship.

The 2012 WGC - Accenture Match Play Championship winner had a chance to help the U.S. tie the 2010 matches and retain the Ryder Cup. He was 2-down with two holes to go against Graeme McDowell. Needing to win the 17th at Celtic Manor to extend the match, Mahan came up short on the 17th, then chunked his chip shot. After McDowell putted to four feet, Mahan missed his par try and he conceded the hole to McDowell, and therefore the Ryder Cup to Europe.

"Like Keegan said, you're nervous (waiting for that call). There are a lot of great players, who could have made this team. You really have no idea, you're just hoping for the best," Mahan said. "It feels amazing. I know these guys had a tough time at Medinah and I had a tough time in '10, so we have a lot to play for on this team."

Simpson will be making his second Ryder Cup appearance. He paired with Bubba Watson for a pair of 5 & 4 wins in fourballs matches in 2012. Simpson earned his ninth top-10 finish the season last week at the Deutsche Bank Championship. The first of those top-10 was a win at the Shriners Hospitals for Children Open.

The 2012 U.S. Open champion was a third-round loser at the WGC-Accenture Match Play earlier this year and missed the cut at three of the four majors.

"There was a lot going on the last few of weeks with the Ryder Cup and me. So many guys that were playing well were going to be good possibilities for a pick. I knew I was in the mix, but I had to play well," said Simpson. "Last week was kind of an emotional roller coaster for me. I didn't really know where I stood when I finished the golf tournament."

Among those that were overlooked included Brandt Snedeker, who played his first Ryder Cup in 2012, as well as last week's winner Chris Kirk, Ryan Moore and Brendon Todd, who all would have been making their first appearance at the Ryder Cup.

"It was a difficult phone call to talk to Chris today. He took it well, he took it like a man," said Tom Watson. "There were several people in the mix for my three picks. As Webb and Hunter said, there are a lot of players starting to play well on the American side. That's a good thing and we're going to need it. Though the European team has been picked as favorites by the pundits, I have a fundamental belief in our team and more importantly, our players have a fundamental belief in themselves that they can go and win the Ryder Cup."

Earlier in the day, European Ryder Cup captain Paul McGinley selected Stephen Gallacher, Ian Poulter and Lee Westwood as his three captains picks.

This year's Ryder Cup will take place at Gleneagles in Scotland from September 26-28.

The European team has won two in a row and five of the last six Ryder Cups. Tom Watson captained the U.S. team to a 15-13 win in 1993 at The Belfry. That was the last U.S. win on European soil.