Modi tweeted two pictures of his with Kovind.
He said, "20 years ago and the present... always been a privilege to know you, President Elect."
"Congratulations to Shri Ram Nath Kovind Ji on being elected the President of India! Best wishes for a fruitful and inspiring tenure," Modi said on Twitter.
"Gladdened by the extensive support for Kovind Ji among MPs and across various states. I thank members of the electoral college," he added.
Modi also said: "I congratulate Meira Kumarji for her campaign, which was in spirit of the democratic ethos and values we all are proud of."
Modi also congratulated opposition candidate Meira Kumar for her campaign.
NDA candidate Ram Nath Kovind was on Thursday elected the 14th President of India, defeating opposition nominee Meira Kumar.