In a message to Putin, Singh wrote, "Your success in these elections is an affirmation by the Russian people of your vision of a strong, prosperous and democratic Russia."
Noting that India and Russia have enjoyed the strongest of relations in recent years, he said New Delhi always recognised Putin as a "special friend" of the country and deeply appreciated the personal commitment and attention that he has brought to nurturing the bilateral strategic partnership over the last 12 years.
Putin, who was the President for two terms earlier, was declared winner in the March 4 Presidential polls.
"It is a matter of great satisfaction that both our countries share a common vision on a range of international issues and that our partnership contributes substantially to international peace and security.
As you prepare to assume your new responsibilities, I look forward to working closely with Your Excellency to strengthen further our strong and close relationship," Singh wrote.
He said he looked forward to welcoming Putin in India later this year for the next India-Russia Summit.