The Russian team won 30 golds and a total of 80 medals during the two-week competition. The next closest team, Ukraine, had five golds and 25 total.
"Thank you very much for the inspiration that you have given millions of people, who are ready to do as you do and not just engage in sport and fitness, but set the highest goals in life," the president was quoted as saying on the Kremlin's website. "You have shown us these high achievements."
Putin presented the athletes with state decorations during a ceremony.
The U.S. finished the Games with a few strong performances over the weekend. The sledge hockey team defeated Russia in the gold-medal match, and Oksana Masters took bronze in the 5-kilometer sitting cross-country race, her second medal of the competition.
In all, Americans won two golds and 18 medals.