The list, which analysed social-media followings, site traffic and overall ability to drive news, also includes British author of the Harry Potter series J K Rowling and singers Taylor Swift and Beyonce.
Time said the Indian Prime Minister has roughly 38 million followers on social networking sites Twitter and Facebook, putting him ahead of any other leaders in the world except Obama.
"And unlike many of his contemporaries, Modi recognises that social media can be invaluable when trying to reach India's 200 million-plus online population directly," the Time magazine said. Modi, an ardent user of social media to communicate with people, announced in an unconventional way, Obama's strategic visit to India in January this year.
He took to Twitter to make the announcement, "bypassing traditional media outlets," the magazine said. Time said given the power of the social media, anyone with a web connection can start a global conversation. "Yes, it helps to be famous in real life. But the rise of social networks has levelled the playing field, allowing unknowns to command audiences rivalling those of real-world leaders, even if by accident," it said.
On Obama's virtual influence, Time said the US President is the most-liked world leader on Facebook and the most-followed on Twitter. "But more impressively, Obama is able to meme himself to push an agenda," Time said citing a video he featured in for American internet news media company Buzzfeed.
In it Obama used a selfie stick among other props to remind millennials to sign up for health insurance under the Affordable Care Act. Within days, the video had been viewed more than 50 million times. The list also includes reality star Kim Kardashian, singer Justin Beiber, actress Gwyneth Paltrow, Chinese actress Yao Chen, singer Shakira, photographer behind the hugely popular blog Humans of New York Brandon Stanton and TV personality Jimmy Fallon.