His predecessor Tony Abbott had visited India in September 2014 and this was followed by Prime Minister Modi's visit to Australia in November that year.
Australia is in the process of exporting uranium, a precious nuclear fuel, to India, but the delayed economic pact between the two nations will reportedly not be signed during the visit.
On energy cooperation, the Indian Prime Minister said that he was happy "that our dialogue and cooperation in other forms of energy, including renewable energy, is on the up-swing".
On education, Prime Minister Turnbull said his government and nation will continue to ensure that we provide outstanding opportunities for Indian students. They also welcomed a decision of holding the first bilateral Army-to-Army exercise, which will take place in 2018. "Australia is looking forward to deepening its bond with India", he added.
Turnbull also introduced the possibility of making progress on the Regional Comprehensive Economic Partnership, which is a multilateral trade agreement between 10 countries, including Australia and India.
Australia is also seen to be important for India's diplomacy, as the latter tries to boost its maritime links and presence in the Indo-Pacific region, against the backdrop of an increasingly assertive China.More news: FA Cup semi-final odds review: bookmakers can't split Chelsea & Spurs
Bilateral trade between India and Australia reached $12.16 billion, nearly double compared to what it was a decade ago.
Besides coal and education, the bilateral trade between the two Indian Ocean Rim countries is increasing at a healthy pace and has doubled to more than A$20 billion in the past one decade. Modi said, "We have just inaugurated the TERI-DEAKIN Research Centre on Nano and Bio Technology, which is a classic example of the kind of cutting-edge science and technology cooperation that is happening between our two countries".
Later, External Affair Minister Sushma Swaraj called on the visiting dignitary.
The duo rode the train from Mandi House station to Akshardham station.
Speaking on the occasion, Rajeev Pratap Rudy, Minister of State (Independent Charge) for Skill Development and Entrepreneurship, said: "For very long, in India, education did not carry the skills along".