Singh in his letter said the sportsman has created a lasting legacy in the world of chess.
"I join the nation in congratulating you on winning the world chess championship for a record fifth time. You have created a lasting legacy in the world of chess and continue to do so with your spectacular performances."
Wishing Anand many more enjoyable years in playing Chess, he said, "You have shown exceptional dedication to the game, a never say die spirit and a steely resolve to carve a niche for yourself in the history of the game. You are truly one of the all time greats."
Anand clinched his fifth world championship title yesterday in Moscow beating Boris Gelfend in a tie-breaker 2.5-1.5 after their 12-game affair ended in a draw.
This was Anand's fourth world title in a row. The Indian chess champion bagged his first world title in 2000 before winning three in a row in 2007, 2008 and 2010.
He has been the world champion since 2007.