Senators said that after Georgia's act of military aggression against South Ossetia, which also reignited the conflict with Abkhazia, Georgia has lost the moral right to seek control of the breakaway provinces.
The offensive "definitively deprived the Georgian leadership of the right to push for the South Ossetian and Abkhazian peoples' dependence on their adventurist polices, which have led to a humanitarian catastrophe," the address to the president said.
Hundreds of civilians were killed in South Ossetia, the regional capital Tskhinvali was devastated, and thousands of locals were forced to flee when Georgia launched an attack on August 8 to seize control of the region, which gained de facto independence after a bloody post-Soviet conflict in the early 1990s.
Russia retaliated with an operation to "force Georgia to peace" which was concluded on August 12. Georgia's ally the United States, along with other Western powers, accused Moscow of disproportionate use of force, and NATO froze ties with Russia last week.
"In view of the repeated requests from South Ossetia and Abkhazia to recognize their independence, including those made on August 22 and 24, the Federation Council proposes that Russia support their independence," the statement said.
All 130 lawmakers present at the session backed the move, which is likely to further strain relations with Western powers, who have called on Russia to respect Georgia's territorial integrity. Russian President Dmitry Medvedev has said the provinces' residents should be given a say in their eventual status.
The lower house of parliament, the State Duma, is expected to approve a similar resolution later on Monday.
Speaking in the Federation Council before the vote on Monday, South Ossetian leader Eduard Kokoity said: "I am asking Russia to recognize South Ossetia as an independent and sovereign state."
Kokoity flew out to Moscow on Saturday to deliver his republic's appeal for recognition, approved by the separatist parliament on Friday.
"What the Georgian leadership has done in South Ossetia can only be described as a Caucasus Stalingrad," Kokoity said.
Abkhazia's president said the two self-proclaimed republics can never be under Georgian control.
"It is hard to say what decision Russia's political leaders will make on our republics, but I can say for certain that Abkhazia and South Ossetia will never be part of Georgia," Sergei Bagapsh told the Federation Council.
"We are requesting that you overcome this barrier, which has for a long time been a difficult thing to do, and recognize our republics as independent states," he said.
Moscow has now withdrawn most its troops from Georgia, but left some personnel at checkpoints on key roads, saying they are needed to deter further bloodshed and protect South Ossetia and Abkhazia.
While the U.S. and other Western powers have called for a full and immediate withdrawal of Russian troops, Russia says a peace deal brokered by French President Nicolas Sarkozky during the conflict allows for "additional security measures" in a buffer zone near South Ossetia, in Georgia proper.