Modi will arrive in Indonesia on Monday and then travel to Australia before ending his trip in New Zealand on July 11, India's foreign ministry said.
After Modi's recent visits to Mauritius and Seychelles and the visit of Japan's Prime Minister Sanae Takaichi to New Delhi this week, the focus has "shifted to the eastern maritime zones of the Indian Ocean and our Act East engagement," Indian foreign ministry official Rudrendra Tandon said.
During the visits, Modi is expected to meet leaders of the three countries - Indonesian President Prabowo Subianto, Australian Prime Minister Anthony Albanese and New Zealand Prime Minister Christopher Luxon.
In Melbourne, Modi is also expected to meet leaders from top Australian companies as well as visit the Melbourne Cricket Ground.
India is one of Australia's largest trading partners, with about a million Indian-born residents making up Australia's largest overseas population.
The visit to New Zealand comes amid rising anti-Indian sentiment in the country and tensions in New Zealand's ruling coalition caused by a free-trade agreement between the two.
"Prime Minister Modi's visit is historic, with this being the first to New Zealand by an Indian Prime Minister in 40 years," New Zealand's Luxon said in a statement on Friday.
New Zealand and India signed a free-trade agreement in April that will eventually remove tariffs on 100 per cent of Indian and 95 per cent of New Zealand goods.