The organisation has pledged support to the countries in an effort to help them modernize their economies following leadership revolts earlier this year.
Robert Zoellick, president of the World Bank, said assistance for Egypt would come in the form of $4.5 billion, with the International Monetary Fund also expected to offer a loan.
A further $1 billion is likely to be made available to Tunisia, he stated, which could be added to a further $500 million in aid that was suggested last month.
Mr Zoellick noted: "The revolutions in the Middle East and North Africa offer great opportunities but also pose daunting challenges and risks."
US president Barack Obama and British prime minister David Cameron have both backed moves for greater financial and political support to be granted to Egypt and Tunisia to help the nations regain stability, the Guardian reports.
By Gary Cooper