Here are the latest developments in this story:
The Prime Minster also announced a two-month deadline for the merger of Overseas Citizenship of India (OCI) and Person of Indian Origin (PIO) status to woo the Indian diaspora. He had announced this at a similar reception in New York's Madison Square Garden during his visit to the US in September, but had not given a timeline then.
Making his first public address in Australia, he exhorted his audience to support his Clean India campaign and talked about cricket and the "cultural history that linked" India and Australia.
PM Modi said the love and honour he was given today is the right of all Indians, not his. He also said, "Mother India has 250 crore arms, 200 crore of those arms are younger than 35. It's the youth of India who can help us fulfill our potential."
To much cheering, he said, "You can take off from India at night and reach Australia the next morning. But it took 28 years for an Indian PM to reach Australia. I promise you will never need to wait that long again." He also promised, "I know that behind this affection lies expectations. Yes. We want to create the India you are dreaming of."
He walked on to the stage amid drum beats, cymbals clashing, wild applause and chants of "Modi, Modi". On stage, PM Modi greeted among others, an Australia-based cartoonist Ramesh Chandra, who is a cancer patient and had requested a meeting.
As he had arrived at the arena, dressed in a white kurta and bright blue half-sleeved jacket, he was mobbed by enthusiastic fans who clamoured for photographs.
Outside the Allphones arena, there was Indian food, people in Modi masks and T-shirts, drummers and dancers. About 5,000 people who could not get tickets to the show inside watched Mr Modi speak on big screens outside the venue.
"Hello Sydney!" said a tweet from the Prime Minister's Office, accompanied by a photo of Mr Modi waving as he arrived at the Sydney airport this morning. At Sydney's Pullman Hotel, four aboriginal dancers performed in welcome and Mr Modi was gifted a boomerang. Mr Modi tweeted a photo and said, "Amazing welcome in Sydney. Glad to be here."
About 220 Modi fans travelled 11 hours from Melbourne to Sydney on a specially chartered train decked in India's national colours, being called the "Modi Express." A special Gujarati meal was served on board the train. There are around 450,000 people of Indian origin in Australia, including many from the student community.
After six hectic hours in Sydney, Mr Modi will leave for Canberra and will then visit Melbourne. After his four-city visit to Australia, Mr Modi will visit Fiji, before returning to India.
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