The prime minister, who leaves on foreign tour Nov 11, in a series of 12 tweets Thursday wrote that he will be travelling to the three countries to participate in various multilateral meetings and summits.
About Myanmar, his first stop, the prime minister said he will be attending two key multilateral summits - with the 10-member Association of Southeast Asian Nations (ASEAN) and the East Asia Summit Nov 12-13 at Nay Pyi Taw, Myanmar's new capital.
Modi said India's ties with Southeast Asia were "deep rooted" and strengthening relations with the ASEAN nations was an important part of his government's 'Act East' policy.
External Affairs Minister Sushma Swaraj has said that the Modi government will strive to give a greater push to India's Look East Policy, turning it into "Acting East".
As part of this, the government has increased its engagements with South and Southeast Asian nations, including through the building of connectivity corridors to boost trade and people-to-people contact.
Modi also said he will have bilateral meetings with the leaders of Myanmar, including President Thein Sein.
He described Myanmar as "a valued friend. Having stronger relations with Myanmar is a priority area for us", he wrote.
Myanmar is virtually the door to India's Look East Policy as it has border connect with four northeast Indian states and most of the connectivity corridors with ASEAN run through Myanmar.
The prime minister said "ASEAN is central to our dream of an Asian century, where India will play a crucial role. Am sure the meetings there would be fruitful".
Modi will also get to meet with the new Indonesia President Joko 'Jokowi' Widodo.
He said he will travel from Myanmar to Australia to attend the G20 meet at Brisbane.
Modi described the G20 as "a great platform to showcase opportunities India has to offer to the world".
Modi also said he looks forward to "working with G20 leaders on important issues concerning the world, particularly those relating to the global economy".
"In Australia, I will meet the country's top leadership & am honoured to have been given an opportunity to address the Australian Parliament," he wrote.
"My Australia visit is both special & historic. It will be 1st bilateral visit to Australia by an Indian PM in 28 years," he wrote.
In 1986, then prime minister Rajiv Gandhi had visited Australia to meet Bob Hawke.
"I am also eagerly looking forward to interacting with the Indian community in Australia," he said.
The Indian expatriate community has planned an enthusiastic Madison Square Garden-like reception for Modi in Sydney Nov 17.
Tickets have been sold out for the event organised by the Indian Australia Community Foundation (IACF) at Sydney's AllPhones Arena.
More than 21,000 people have already registered through their local community organisations to attend the event in Sydney, which can only seat 16,000.
Modi will address the Australian parliament Nov 18 in Canberra, the first Indian prime minister to do so.
Among the host of world leaders coming to Australia for the G20, only three will address the federal parliament -- China's Xi Jinping, Britain's David Cameron and Modi.
Commenting on cricketing ties between India and Australia, Modi said: "Cricket is a shared passion of Australia & India. I thank PM @TonyAbbottMHR for hosting me at the iconic Melbourne Cricket Ground."
It will be the second time in three months that Abbott and Modi are meeting.
The Australian Prime Minister was the first head of state to be received in India by the new government when he arrived in New Delhi in September.
"Both Australia & India fought shoulder to shoulder during WW1. I would be visiting the War Memorial with PM @TonyAbbottMHR," he tweeted.
Modi flies to Fiji from Australia, where he would meet Prime Minister Frank Bainimarama. He returns Nov 20.