Manmohan Singh is beginning an official visit to Burma, the first by an Indian prime minister since 1987.
Mr Singh said he hoped to strengthen trade and diplomatic co-operation during his three-day trip.
He will meet President Thein Sein and opposition leader Aung San Suu Kyi, whose mother once served as Burma's ambassador to India.
The two nations share a 1,600km (1,000 mile) border, but relations have often been uneasy.
The Delhi government cold-shouldered Burma's military rulers during the 1990s, infuriating the generals by openly supporting Ms Suu Kyi.
But Mr Singh has overseen a dramatic turnaround in Delhi's policy, and controversially hosted former ruler Than Shwe on a state visit in 2010.
Before his current visit, Mr Singh said he wanted "stronger trade and investment links, development of border areas, improving connectivity between our two countries and building capacity and human resources".
Analysts say India is desperate to counteract the influence of China in the region, and Mr Singh will be keen to stress the close cultural and historical ties between the two countries.
India has already signed a number of deals for the exploitation of Burma's vast reserves of natural gas, and Indian firms are building ports and other infrastructure projects in Burma.
A high-powered business delegation will join Mr Singh's entourage, including telecoms tycoon Sunil Bharti Mittal, chairman of mobile giant Bharti Airtel.
Last week, India made a symbolic announcement that transport links would be improved, including the first official bus route across the border.
India is now Burma's third biggest export market, behind China and Thailand.
But China still dominates oil and gas exploration in Burma and is involved in the construction of roads, pipelines and port facilities.
And the Burmese government's recent reforms have ended the country's international isolation, which means Western nations are joining the rush to invest.