Sochi bid leader Dmitry Chernyschenko told Reuters: "We are happy and satisfied and we owe a huge debt of gratitude to the IOC."
Vladimir Putin, the Russian president, travelled to Guatemala to lobby for Sochi.
He owns a holiday home in the area and is often seen skiing on the Krasnaya Polyana mountains.
Located 1,500km south of Moscow
Population about 400,000
$1.5bn budget for both 2014 Olympic and Paralympic Games
Estimated 19,000 security personnel
To build all 11 Games venues
Russia, an Olympic power which has won 293 Winter Games medals, has never hosted the Games.
That was a strong point in Sochi's favour with the IOC, which likes to spread the Olympics to new host countries.
Moscow staged the Summer Games in 1980 which were hit by the US-led boycott following the Soviet invasion of Afghanistan.
Sochi proposed a concept based around an ice cluster in the form of an Olympic park just outside the city, and a mountain snow zone in the Krasnaya Polyana range.
During the bidding, Salzburg presented itself as a safe, no-risk winter sports hub at the heart of Europe with world-class venues already in place.
Pyeongchang offered the potential for peace and reconciliation on the divided Korean peninsula and promoting winter sports in Asia.
Sochi had lost to Salt Lake City in a bid to host the 2002 Winter Games previously.
Pyeongchang, which narrowly lost four years ago to Vancouver for the right to stage the 2010 Games by just three votes, was devastated to lose again.
"It's almost like being stabbed in the back," said Jeon Yong-kwan, the bid development director. "I don't get it. We did everything the IOC asked of us."