England and Russia plus two joint bids from Netherlands/Belgium and Spain/Portugal were contesting the 2018 finals.
The announcement of the winning bid was made by FIFA president Sepp Blatter at Zurich's Messezentrum.
Russia and Qatar, who will stage the 2022 finals, are both first-time hosts.
Blatter said: "We go to new lands. Never has the World Cup been in Russia and Eastern Europe, and the Middle East and Arabic world have been waiting for a long time so I'm a happy president when we talk about the development of football."
Russia deputy prime minister Igor Shuvalov, whose delegation whooped with delight on the announcement, said: "You have entrusted us with the FIFA World Cup for 2018 and I just can promise, we all can promise, you will never regret it. Let us make history together."
Russian Prime Minister Vladimir Putin said he was leaving for Zurich to thank FIFA.
"This decision shows that Russia is trusted," Putin said before leaving for the airport to fly to Zurich.
Putin, who had complained of unscrupulous competition in the contest, said the decision showed much about Russia's economic and political stability.
"Hurrah! Victory!," Russian President Dmitry Medvedev said in a Twitter post on the FIFA decision.
Finance Minister Alexei Kudrin said Russia will spend significantly less on preparations of the 2018 World Cup than on the organisation of the 2014 Winter Olympics.
"It'll be significantly less," Kudrin said. "We have a clear plan on assigning sites."
The 22 men on FIFA's executive committee heard half-hour presentations from each of the four competing European bids this morning.
Russia presented itself as a huge nation which had never before staged the World Cup, contrasting it with western Europe where all the major nations have staged the event.
Alexei Sorokin, the Russian bid's CEO, began by quoting Winston Churchill's famous description of Russia as "a riddle wrapped in a mystery inside an enigma."
He said: "We can understand this perception that foreigners have but it's a Russia...that no longer exists."
England may have suffered from a backlash against corruption investigations into FIFA members by BBC Panorama and the Sunday Times over the last two months. These investigations were criticised both by Russian prime minister Vladimir Putin and Spain/Portugal bid president Angel Villar Llona in his presentation to fellow FIFA members on Thursday.
Six FIFA officials were last month suspended following a Sunday Times investigations and on Monday, BBC Panorama claimed three other FIFA members had taken bribes in the 1990s.
The defeat comes despite an impressive presentation by England that was described by Blatter as "excellent and remarkable".
Prince William, David Cameron and David Beckham all sparkled but were all outshone by 27-year-old Eddie Afekafe, who works on Manchester City's community programmes.
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