A spokesman for the Rosoboronexport agency responsible for foreign military contracts said India had informed Russia of the decision earlier in the week.
The official added that no formal explanation was given for the decision and that the choice "was the exclusive right of India".
The US ambassador to New Delhi on Thursday said Washington was "deeply disappointed" that Lockheed Martin's F-16 and Boeing's F/A-18 Super Hornet had also been rejected.
India has made no official announcement but the US and Russian confirmations indicate that only the Dassault Rafale fighter of France and the joint Eurofighter Typhoon project are still in the running.
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