It said the funds can be used to develop infrastructure, schools or other projects.
Burma has introduced political and financial reforms recently, prompting various countries to lift their sanctions against it.
The World Bank said the grants were “intended to build confidence in the reform process”.
“We are committed to eradicating poverty,” Jim Yong Kim, World Bank group president, said in a statement.
“They have been cut off from the global economy for too long and it’s very important that they receive real benefits from the government’s reforms.”
The bank said that it would also help to restructure the payment of Burma’s current arrears of $397m.
Once that amount has been cleared, Burma will also be given access to interest-free loans from the International Development Association, the World Bank’s fund for the poorest countries.
The bank, which has opened up an office in Burma, said that it would also provide assistance to Burmese authorities, so that the country could further reform its financial system and improve the business environment.
“Actions in these areas will help the government attract responsible foreign investment, expand trade, manage its resources better and create more jobs and opportunities for people,” said Pamela Cox, vice-president for East Asia and the Pacific.
Meanwhile, the International Finance Corporation, a member of the World Bank that focuses on private sector development, said it had started conducting an assessment to see which areas of the economy needed further support.