The document said: "[With] absent compelling evidence to the contrary, this leads to the conclusion that the aircraft belonged to the Russian air force."
Russia's defence ministry has rejected the UN's conclusions, saying "planes of Russian air forces made no flights near Georgia's border on April 20".
"There can't be any talk of any violation of Georgia's state border, to say nothing of shooting down an unmanned aircraft," said Alexander Drobyshevsky, a ministry spokesman.
Russia had previously said that the drone was shot down by anti-aircraft batteries operated by Abkhazian separatists.
Mikheil Saakashvili, Georgia's president, said the UN report was "the first-ever case when an international organisation ... pointed at Russia for such actions".
The report contained "a direct accusation against Russia of an act of aggression," he said.
The UN document also criticised Georgia over the spy plane incident, saying flying surveillance aircraft over Abkhazia was in violation of a 1994 Moscow Agreement ceasefire.
The report said: "It stands to reason that this kind of military intelligence-gathering is bound to be interpreted by the Abkhaz side as a precursor to a military operation, particularly in a period of tense relations between the sides."
But it said that was no justification for Russia shooting down a Georgian plane.
"Enforcement action by third parties, in this case the Russian Federation, in the zone of conflict is fundamentally inconsistent with the Moscow agreement and ... undercuts the ceasefire and separation of forces regime."
Georgian officials had previously released a video, recorded by the spy plane's onboard camera before it was shot down, which showed a MiG-29 Russian fighter plane approaching it and then launching a missile in its direction.
Moscow and Tbilisi are locked in a bitter dispute over Russian support for Abkhazia and South Ossetia, who wish to breakaway from Georgia, and Saakashvili's ambitions for his country to join Nato.
Abkhazia is recognised internationally as part of Georgia, but it has run its own affairs since it drove out Georgian forces in a separatist war in the 1990s.
Russia provides assistance to the separatists and has peacekeepers in Abkhazia, prompting Tbilsi to accuse Moscow of a creeping annexation of the region.