The Indians who draw crowds of adoring fans are usually tall and sultry, with washboard abs and elaborate outfits, Bollywood stars like Shah Rukh Khan — described by some as the Brad Pitt of India — or Priyanka Chopra, the bombshell actress, singer and model.

But this time it is a teetotaler and bachelor who has boasted of his 56-inch chest and wears a simple cotton shirt.

Narendra Modi, India’s new prime minister, will receive a rally fit for a rock star at Madison Square Garden on Sunday. His rags-to-riches story mirrors the rise of Gujarat, the Indian state that he governed and that gave him and his Bharatiya Janata Party a landslide victory in India’s general election in May. His new profile has also allowed him to return to the United States for the first time in more than two decades; the State Department had revoked his visa in 2005 over his alleged role in deadly religious riots in Gujarat three years earlier.

For Mr. Modi and his supporters, the visit, which includes a speech before the United Nations General Assembly and a meeting with President Obama, is also a moment to connect with members of the broad Indian diaspora in the United States, many of whom watched with embarrassment from afar as India’s economic engine sputtered and corruption scandals plagued Mr. Modi’s rivals in the Indian National Congress party, which has governed India for most of its postcolonial history.