International team captain Gary Player used his two picks on K.J. Choi of South Korea and Tim Clark of South Africa, who was tied for the lead at the PGA Championship on Sunday before finishing third.
'I felt the stability of a couple of older players would help my team,' Nicklaus said.
The Presidents Cup, to be played Nov. 20-23 in South Africa, is patterned after the Ryder Cup and matches the United States against an International team made of countries all over the world except Europe.
The United States leads the series, 3-1, and is coming off a 21 1/2-10 1/2 victory three years ago at the Robert Trent Jones Golf Club in Virginia.
Nicklaus chose the 11th and 12th players in the standings the last time he was U.S. captain in the Presidents Cup, in 1998 at Royal Melbourne in Australia. The Americans absorbed their worst loss ever in team match play, 20 1/2-11 1/2.
The 47-year-old Funk tied for seventh in the PGA Championship and retained his 11th spot in the standings. Haas, 49, closed with rounds of 69-69 on the weekend and tied for fifth, moving up three spots to No. 16 in the standings.
By selecting Haas, Nicklaus passed over Bob Estes at No. 12 in the standings. Estes has never played in either a Ryder Cup or Presidents Cup, narrowly missing out in 1999.
Nicklaus, whose career is defined by 18 major championships, also passed over British Open champion Ben Curtis and PGA champion Shaun Micheel. Neither had won a PGA Tour event until capturing those majors.
The Americans will have four players who have never experienced team matches - Chris DiMarco, Jerry Kelly, Charles Howell III and Funk.
'I felt like if I was going to select Ben Curtis or Shaun Micheel, I would like to have both of them,' Nicklaus said. 'Chad Campbell also was very deserving.'
Haas played in the 1983 and 1995 Ryder Cup and the 1994 Presidents Cup. While he hasn't won, Haas is having one of his best years on tour, 10th on the PGA Tour money list with $2.2 million.
'Jay has had a wonderful year,' Nicklaus said. 'He had a good PGA Championship, and he has a lot of international experience. We had three fellows on this team that do not have that experience. The stability Jay brings to the team will be important on foreign soil.'
Estes lobbied hard over the week to be included, saying he has consistently been ranked around No. 20 in the world over the last two years.
Estes also was bypassed for the Ryder Cup team in 1999.
Nicklaus said he will announce an assistant captain on Wednesday - a player who would be the alternate in case someone gets hurt or decides not to travel to South Africa the week before Thanksgiving.
The rest of the U.S. team includes Tiger Woods, Davis Love III, Jim Furyk, David Toms, Kenny Perry, Phil Mickelson and Justin Leonard.
The International team will have Ernie Els, Vijay Singh, Mike Weir, Nick Price, Retief Goosen, Robert Allenby, Stephen Leaney, Peter Lonard, Adam Scott and Stuart Appleby.
Choi was 11th in the standings, and Player called him one of the most consistent players.
'He has showed that consistency on the most difficult tour in the world,' Player said, noting that Choi was a two-time winner on the PGA Tour last year.
Clark was somewhat surprising.
He was 23rd in the standings, but his 68-69 weekend at Oak Hill for a third-place finish moved him up to No. 16.
Player passed over Eduardo Romero of Argentina, Michael Campbell of New Zealand, Angel Cabrera of Argentina and Trevor Immelman of South Africa.
Clark's selection gives the International team three South Africans, along with Price, who is from Zimbabwe; and five Australians. No Japanese players will be on the team for the first time since the Presidents Cup began in 1994.
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