Mr Modi received a thunderous welcome as a crowd of 16,000 adoring fans cheered his arrival on stage at Sydney's Super Stadium.
Members of the Indian community from across Sydney and as far afield as Melbourne erupted in chants of "Modi, Modi, Modi" as the white-bearded 64-year-old appeared.
It was the first time in 28 years an Indian Prime Minister has visited Australia.
Mr Modi dedicated the welcome to the people of his home country.
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After acknowledging the traditional Indigenous owners of the land in English, Mr Modi continued in Hindi.
"This love, this welcome, this respect I give to the children of Mother India," he said.
The arena again erupted in cheers as one man in the audience yelled out "Modi the rock star!".
Eight Indian TV broadcasters are covering the event and beaming it across India.
The Indian PM's appearance was preceded by an elaborate stage show of costumed dancers and thundering traditional beats from a Campbelltown-based Indian drumming group.
With all free tickets to the event snapped up, hundreds more people watched the proceedings on a huge outdoor screen.
Susan Mathew from Liverpool, was among those who missed out on tickets but had come anyway.
"People are feeling that there will be some changes that will be positive for everybody," she said.
"We just thought we would come here and enjoy the scene Rakish Chand, from Penrith was born in Fiji but said he felt hope with the arrival of Modi.
"I've seen decades of moral decay and corruptions in India," he said.
"We find there's a change with Modi."
NSW Premier Mike Baird and his predecessor Barry O'Farrell were among Australian dignitaries present on stage to welcome Mr Modi.
Australian cricketing great Brett Lee was also there to meet the visitor.
