Modi also congratulated opposition nominee Meira Kumar for her campaign, saying it was "in the spirit of democratic ethos and values we all are proud of".
Kovind, a 71-year-old BJP leader who was the NDA candidate, defeated Kumar, former Lok Sabha Speaker, with an overwhelming majority to become the country's 14th President.
"Congratulations to Shri Ram Nath Kovind Ji on being elected the President of India! Best wishes for a fruitful & inspiring tenure," the prime minister tweeted immediately after the results came in.
Kovind got 65 per cent of the votes in the electoral college comprising MPs and MLAs.
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