Pavin had said last month that he was not guaranteed a place because he wanted to be fair to all the players in contention.
Woods has played in five Ryder Cups beginning at Valderrama in 1997 but missed out in 2008 after knee surgery, when the US team won for the first time since 1999 and recorded its largest margin of victory since 1981.
In 25 Ryder Cup games, he has never been left out of a single match, winning 10, halving two and losing 13.
"I always love playing in Ryder Cup, being part of the team," Woods said. "It is an experience you will never forget.
"It is one of those things I have been looking forward to. It is nice my game is coming around.
"I feel my game is not very far away. It makes it a lot easier going into a pressure-packed environment."
Pavin's other three picks feature two major winners in Johnson and Cink, while the 21-year-old Fowler is one of the most exciting prospects in the game.
Johnson, 34, the 2007 Masters champion, finished third in the US PGA last month and returns to the side after making his debut at The K Club in Ireland four years ago.
The 37-year-old Cink was picked for the third time in four matches despite not winning a tournament since his Open triumph last year, and claiming only one top-10 finish in the last six months.
Fowler, at 21 the same age as Rory McIlroy, becomes the first player to advance from the Walker Cup to the Ryder Cup in just one year.
Like my European team, the American side has an excellent blend of youthful talent
Europe captain Colin Montgomerie
Pavin said he had a "gut feeling" about the youngster, who has three second places on the US Tour and has moved up to 33rd in the world.
Fowler, the third youngest American to play in the Ryder Cup, said: "It was hard to sleep last night but this is awesome to be selected.
"I have to thank Corey for giving me the opportunity to go over there, being a young player, it is a pretty special opportunity."
He was preferred to Anthony Kim, who was one of the stars of the US team in 2008, winning twice, losing once and halving once in four matches.
Kim, though, has missed three months this year because of thumb surgery and was bumped out of the top eight automatic slots in the last qualifying event.
Lucas Glover, the 2009 US Open champion, was also overlooked despite finishing 10th in the qualifying race, while big-hitting JB Holmes, who made his debut at Valhalla two years ago, and rising stars Nick Watney, Ricky Barnes and Ben Crane also missed out.
Montgomerie, who named his
after the Johnnie Walker Championship on 29 August, added: "Corey has used his four captain's picks to good effect as I knew he would.
"I am glad we now know the 12 men we will face at Celtic Manor. Like my European team, the American side has an excellent blend of youthful talent."
The US will be vying for their first victory on foreign soil since 1993 when the 2010 edition takes place from 1-3 October in south Wales.
"I wish the American team safe travels and we all look forward to welcoming them to Wales," Montgomerie added.
RYDER CUP TEAMS Europe: Luke Donald (England), Ross Fisher (England), Peter Hanson (Sweden), Padraig Harrington (Ireland), Miguel Angel Jimenez (Spain), Martin Kaymer (Germany), Graeme McDowell (Northern Ireland), Rory McIlroy (Northern Ireland), Edoardo Molinari (Italy), Francesco Molinari (Italy), Ian Poulter (England), Lee Westwood (England).
United States: Stewart Cink, Rickie Fowler, Jim Furyk, Dustin Johnson, Zach Johnson, Matt Kuchar, Hunter Mahan, Phil Mickelson, Jeff Overton, Steve Stricker, Bubba Watson, Tiger Woods.
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