The Russian President called the Norwegian world number one a "genius" and awarded him his prizes during the ceremony.
“First of all, I want to congratulate Magnus Carlsen with a well earned victory. I also want to thank Anand for his honest competition. It was a fair fight that was followed by millions of viewers from more than 100 countries,” said Putin.
Carlsen received a large victor's goblet, a laurel and a medal weighing almost one kilo. The Norwegian takes home prize-money of 5.3 million kroner ($778,000).
Putin said to VGTV: “Magnus Carlsen is a genius. I’m impressed by what the Norwegian achieved during the Championship.”
Russia's leader took time after the award ceremony on Tuesday to sign autographs and let himself be photographed with Carlsen and a number of children who were invited to the event. Then Putin went, following Russian tradition, to drink tea together with Magnus Carlsen, Vishy Anand and their families.
Magnus Carlsen said in his speech of thanks: "I want to thank the organizing committee. We have been treated in the best possible way.”
The Norwegian winner said: "Thanks to my team, my personal assistant, my father, Espen (Carlsen's manager), and the rest of my family, the chef and the doctor. I also want to thank my competitor Vishy Anand, who made it a tough fight to the very end. I wish him all the best in the future.”
Carlsen added: "I also thank all chess fans who followed our games all over the world. This victory goes to you.”
The victory ceremony in Sochi was delayed because Putin arrived late.
On Sunday, Carlsen will celebrate his 24th birthday by, among other things, playing 16 matches in Oslo against teams consisting of Norwegian celebrities, politicians, and ordinary people.