The credit line will have a ceiling of 400 million reais per stadium, limited to 75 percent of the total cost of the projects, the BNDES said in a statement after a meeting between President Luiz Inacio Lula da Silva and ministers linked to Brazil's staging of the tournament.
None of the 12 stadia put forward by Brazil for the tournament currently meet FIFA's criteria for World Cup grounds.
The Maracana, which will probably hold the final, will be closed from next year for modernisation work, while most of the rest will be practically rebuilt. Two new grounds will be built in Recife and Natal.
Of the 12 stadia, only three belong to clubs: Morumbi, home of champions Sao Paulo, and two in the southeast of Brazil, Atletico Paranaense's Arena da Baixada in Curitiba, and Internacional's Beira Rio in Porto Alegre.
The remainder are publicly owned.
The BNDES said funding would depend on factors like urbanisation plans in the areas surrounding the grounds and promotion of sustainable technology.
The release of public funds for the work contradicts a promise made by the tournament organisers when Brazil won the right to stage it as South America's sole bidders.
The original plan had been for private enterprise to look after the stadiums, leaving the state to work on infrastructure.
The BNDES had already approved five billion reais credit for improvements in transport, particularly the airports at venue cities.
Belo Horizonte, Brasilia, Cuiaba, Curitiba, Fortaleza, Manaus, Natal, Porto Alegre, Recife, Rio de Janeiro, Salvador and Sao Paulo will host matches at the 2014 tournament.
