Each sport received majority support in separate votes after presentations by leading athletes and officials.

Rugby will organise a seven-a-side tournament for 12 men's and women's teams. 

Golf will stage a 72-hole stroke-play tournament for men and women.

Members voted 63-27 for golf, and 81-8 in favour of rugby.

Tiger Woods and some of the world's leading golfers urged the IOC to include the sport on the Olympic programme.

Woods, who is playing at the President's Cup in the United States, appeared in a video message in which he said it would be "an honour for anyone who plays this game to become an Olympian."

The vote brings the number of summer Olympic sports back to 28. 

Golf and rugby were added for the 2016 Olympics and 2020 but will be reviewed in 2017.

There have been two openings on the programme since baseball and softball were dropped in 2005 for the 2012 London Games.

Rugby last appeared in the 1924 Olympics in the full 15-a-side format. 

Golf was played at the 1900 and 1904 Games.

They are the first sports to be added to the Olympic since taekwondo and triathlon made their debuts at Sydney in 2000.

Jacques Rogge, the President of the IOC, said: "Both golf and rugby are very popular sports with global appeal and a strong ethic.

"They will be great additions to the Games."

The two sports, voted on separately in alphabetical order of the sports, golf then rugby, only needed a simple majority of votes cast by the members of the Session. 

The result of the first vote was not revealed to the Session until the vote for the second sport had taken place. 

Peter Dawnson, the secretary general of the International Golf Federation (IGF), said:  "The International Golf Federation is absolutely delighted by today’s results. 

"We thank the IOC for the thorough process and we are looking forward to playing our part as a member of the Olympic Movement.

"This is great for golf and we hope to be of great benefit to the Olympic Games as well.”

Bernard Lapasset, the President of the International Rugby Board (IRB), said: "I am so delighted and proud. 

"My thanks to the IOC members for their wonderful support. 

"Rugby is honoured to be a part of the Olympic Sports Programme and we are already looking forward to Rio 2016."

Golf was played at the Games in 1900 in Paris and in 1904 in St Louis, while rugby was part of the programme of four editions of the Games between 1900 and 1924.

In addition to the two new sports, the Session also voted to accept the list of 26 core sports on the programme for the Olympic Games in 2016.