Modi's Twitter account @narendramodi has 4,240,643 followers, with a weekly increase of 6.77 per cent, monthly increase of 12.22 per cent and quarterly growth of 24.26 per cent, says the report.
The most followed world leader on Twitter is US President Barack Obama, followed by Pope Francis. Obama has over 40 million followers on Facebook and Modi is the second most popular politician in the world. The Indian leader has greater growth rate on Facebook (1.171 per cent) compared to Obama's 0.305 per cent.
Modi has overtaken Mitt Romney, the former Republican presidential candidate, who now has 11.345 million followers on Facebook.
Modi is one among the three persons whom Japan premiere Shinzo Abe follows on Twitter.
Twiplomacy is New York-based Burson-Marsteller's annual study. It attempts to find out the extent to which world leaders use Twitter, a popular social networking site.
Earlier, Facebook had said that Narendra Modi's account is the fastest growing Facebook page for any elected leader in the world.