"If we put it straight, there has been no such event in the contemporary history of our country which would so much consolidate our nation, our people," Prime Minister Dmitry Medvedev told athletes at the handover ceremony held near the Kremlin.
"You gave us this feeling of pride, you didn't do it on an ordinary day, but rather when the Olympic Games were held in our country."
Russia won 13 gold, 11 silver and nine bronze medals at the Games, which ended on Sunday. President Vladimir Putin staked his political reputation to hold a successful Games aimed to show the world the modern face of Russia and boost patriotic sentiment.
IOC bans 11 Russian winter athletes for life for Sochi 2014 doping
Last week the Kremlin chief handed state awards to the athletes in Sochi saying that they have "accomplished the mission" assigned to them.
The cars were provided by Russia's Olympic athletes support fund, an entity chaired by Medvedev which has senior officials and billionaires on its supervisory board.
Russian Winter Olympics winners in Turin got Toyota and Lexus cars in 2006 and Audi vehicles after the Games in Vancouver in 2010.
The Sochi Games won praise from International Olympic Committee officials and there were no major security incidents, despite fears following suicide bombings in southern Russia in December blamed on insurgents based in the adjacent North Caucasus restive region.
IOC bans three more Russian athletes for life over doping
IOC bans three Russian bobsledders for life over doping