The Georgian Dream party secured a victory over the United National Movement party of President Mikheil Saakashvili this week. Saakashvili, accused of monopolizing power following a 2004 revolution, said he'd move his party into the opposition.
Saakashvili was criticized for going to war with Russia in 2008 over the disputed territories of Abkhazia and South Ossetia and cut diplomatic ties to Moscow.
Alexander Krylov, a regional expert at Russia's Institute of World Economy, told state-run news agency RIA Novosti ties between both countries shouldn't change dramatically.
"Relations will improve because they can't get any worse," he said.
Saakashvili remains in power until October 2013. The country's government will shift to a parliamentary system after those elections.
U.S. Secretary of State Hillary Clinton said Washington supported reports from European observers that the election was fair.
"Now that the people of Georgia have spoken, the United States encourages all parties to work together constructively in the new Parliament to advance Georgia's democratic and economic development," she said in a statement.