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The summit level talks between the two leaders are expected to focus on trade, energy and security, including the fight against the dreaded terror group Islamic State.
The two countries are also expected to sign a series of pacts on social security, transfer of sentenced prisoners, combating narcotics trade, culture and tourism.
The deal on social security is expected to make it easier to swap staff between the two countries and is likely to boost two-way investment.
The memorandum on tourism comes after PM Modi and Mr Abbott met in September for summit-level talks in New Delhi. They had agreed to begin talks on an agreement on work and holiday visas.
Mr Modi had reached Canberra late in the night and in a departure from protocol, was received by Australian foreign minister Julie Bishop. On Tuesday morning, he visited the Australian War Memorial with Mr Abbott.
The personal relationship between the two was strengthened when the Australian Prime Minister handed back two stolen antiquities to India - the idols of Shiva Nataraja and Ardhanariswara. The idols had been inadvertently bought by Australian galleries.
The visit to Canberra comprises the third leg of the Prime Minister's Australian tour - the first by an Indian Prime Minister in 28 years. He has been to Brisbane, where he attended the G20 summit, and Sydney, where he addressed a 20,000-strong crowd from Olympic Park.
In his first public address in Sydney, PM Modi promised a visa-on-arrival facility for Australian tourists soon, exhorted his audience to support the Clean India campaign and talked about cricket and the "cultural history" that links India and Australia.
PM Modi said the love and honour he was given is the right of all Indians, not his. There are around 450,000 people of Indian origin in Australia, including many from the student community.
The Prime Minister is expected to leave Canberra for Melbourne around 12.30 pm local time. After his four-city visit to Australia, he will visit Fiji, before returning to India.
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