The two sides agreed to play the Group F match on August 14 during this week's meeting at FIFA headquarters in Zurich.
The decision means Russia will have to cancel their high-profile friendly against Lionel Messi-led Argentina in Moscow to make room for the Belfast game.
The Russians had offered to play the Irish on June 11, four days after facing their main rivals Portugal in Lisbon.
Fabio Capello's team top Group F on 12 points after winning all four of their opening matches. Portugal and Israel both have 11 points from six games.
Northern Ireland are a distant fourth with three points from four games and only an outside chance of reaching next year's finals in Brazil.