Up to 40 institutions are lining up to open offices in the country, even as the central bank is set to impose tough operational restrictions.
Burma is undergoing major economic reforms and liberalisation in the process of transition from a military towards a civilian government since 2011.
The economy had faced a long period of isolation because of global sanctions under the former military leaders that left the finance and banking sector little advanced from when the armed forces first took power in the 1960s.
The entry of foreign banks is seen as a major driver to boost the economy and encourage much-needed foreign direct investment.
Central bank deputy governor Set Aung said between five and 10 foreign banks would be issued with licences to open limited banking services from September.
ANZ has had an office in Burma since June 2013.
Local banks and politicians have sought to stall the reform process, which they see as a threat to their market share. But their efforts have failed, with President Thein Sein insisting the reforms go ahead.
Sean Turnell, a professor of economics at Sydney's Macquarie University, said economic liberalisation had been slowed by the crony-capitalists and their strong hold on the economy.
Foreign banks will face tough restrictions in offering services only in United States dollars and not in the local currency, the kyat.
Burma remains one of the poorest countries in Asia.
Most people rely on informal banking in a country with 80 per cent getting by on $5.80 a day. AAP
source: The New Zealand Herald