The discussions between Prime Minister Narendra Modi and Prime Minister Turnbull and the six agreements signed reflect global changes. "Our ties. will be stronger because of this visit", he said.
Mr Turnbull said the formal sports partnership was a key priority for his Indian counterpart Narendra Modi.
In December a year ago, Australian Parliament passed a law to allow the supply of uranium to India.
Turnbull, who arrived in the country on Sunday, also said that Australia was looking forward to exporting uranium to India as soon as possible.
"Now we are working with India to secure timely conclusion of a quality Regional Comprehensive Economic Partnership, the RCEP, which would provide a significant boost to regional confidence".
India and Australia on Monday made a decision to kick-start the stalled negotiations on the Comprehensive Economic Cooperation Agreement (CECA) by holding the next round of talks soon.More news: Giants place Buster Posey (head) on concussion disabled list
It groups the 10 members of the Association of Southeast Asian Nations and a further half-dozen countries, including India, with which ASEAN has free trade deals. He said "my trip has been all about deepening more engaged collaboration between Australia and India in the fields of economics, sports, health, science and education".
The two leaders have also talked about energy with the Australian leader promising that his country can supply uranium to India at any time.
Meanwhile, Minister for Education and Training Simon Birmingham, who is accompanying Turnbull on the visit, said Australia will showcase its worldwide education, training and research offerings during the visit to help it in its goal of upskilling 400 million people by 2022.
Earlier on Monday, Turnbull was accorded a ceremonial welcome at Rashtrapati Bhavan here.
Following the exchange of agreements, Modi and Turnbull via video-conferencing jointly inaugurated the TERI-Deakin Nanobiotechology Centre (TDNBC) at TERI's Green Campus in Gurugram, Haryana. On Tuesday, Turnbull will visit Mumbai, India's financial and entertainment capital, before flying to Sydney, according to India's External Affairs Ministry.