World number one Woods would play at the 2016 Olympics
Golf is set to return to the Olympics after a 112-year absence in 2016, and rugby sevens will also be recommended to be part of that year's Games.
The International Olympic Committee's executive board voted to include both at its Berlin executive board meeting.
The recommendation must be rubber-stamped by a full meeting of the IOC congress in Copenhagen in October.
Softball, squash, baseball, karate and roller sports were also hoping to be included, but have all missed out.
Golf was played at the Paris Games in 1900 - when Walter Rutherford and David Robertson won silver and gold respectively for Great Britain - and four years later in St Louis, but has never returned to the Olympic agenda.
One of the main issues has been whether top players will compete in the Olympics when they already have a full schedule, but superstar Tiger Woods indicated on Tuesday he would play.
The proposed format would be a 72-hole strokeplay competition for men and women, with 60 players in each field. The world's top 15 players would qualify automatically, and all major professional tours would alter tournament schedules to avoid a clash with the Olympics.
IOC president Jacques Rogge said winning an Olympic gold medal would remain one of the main ambitions for top golfers, despite the traditional lure of the four major championships - the Masters, the Open, the US Open and the USPGA.
Rogge said: "This is the young generation that will be at its peak in 2016. The same question was raised time and time again when tennis and ice-hockey were introduced.
Ask Rafael Nadal and Roger Federer, ask the NHL players, ask the NBA basketball players. They all want to go to the Games
IOC president Jacques Rogge
"Ask [top tennis players] Rafael Nadal and Roger Federer, ask the NHL players, ask the NBA basketball players. They all want to go to the games - they are absolutely not concerned about that."
Peter Dawson, chief executive of the Royal and Ancient club and co-leader of golf's Olympic bid, described Thursday's news as "a historic moment for golf."
He went on: "It will be a huge grow-the-game opportunity for us, not just be in countries where golf is already big but in those countries in eastern Europe and Asia where golf is relatively small.
"We were able to show the IOC footage of all the top men and women players coming out in support. We will put the Olympics right at the forefront of golf. It is going to add to golf, no doubt about that."
Ty Votaw of the US PGA added: "We presented a very compelling case for our sport to be included. We have had unprecedented, unified support across the entire golfing world."
And European Ryder Cup 2010 captain Colin Montgomerie said: "I heard that Tiger will play, and I'm delighted he's put his name forward."
Rugby union, which was played in four different Olympics between 1900 and 1924 in the full 15-a-side format, proposes the seven-a-side version for both men and women.
The International Rugby Board would scrap its Sevens World Cup to ensure the Olympics is the sport's top event. Sevens rugby is already part of the Commonwealth Games.
Rob Andrew, elite rugby director at the RFU, said: "Rugby Union is played in more than 100 countries and has a superb opportunity to further develop and grow through its new partnership with the IOC.
"This is a massive boost for the sport, which will raise its profile, encourage more and more people to play and watch the game at all levels not only in England but worldwide."
Welsh Rugby Union group chief executive Roger Lewis said: "The lure of winning an Olympic medal will inspire participation in sevens and 15-a-side rugby at all levels.
Squash laments Olympic omission
"Here in Wales we are currently World Cup sevens champions and I know we have the players to compete for inclusion in any team selected to represent the United Kingdom."
World Squash Federation President N Ramachandran said the whole sport was "hugely disappointed" after being rejected.
He added: "I believe that squash has come a long way in the last four years, not just in order try and gain Olympic inclusion but for the benefit of the sport as a whole. We have invested in developments and listened to players at all levels in order to help progress the sport."
The 15-member board selected the proposed sports for 2016 by secret ballot over several rounds, with the sport receiving the fewest votes eliminated each time. Rogge, who chairs the board, did not vote.
Rugby was the clear winner overall, getting seven votes in the first round and a majority of nine in the second. In a separate ensuing vote, golf needed four rounds to get through.
Karate actually led the first round with five votes, with golf getting three. Golf then got six votes in the second, seven in the third and nine in the fourth.
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