He also revealed that ministers would extend the Code of Practice on Access to Government Information to more than 150 quangos.
The code commits the non-departmental and advisory bodies to give the public facts and analysis about policy decisions. It also sets guidelines for dealing with the public and requires the organisations to give reasons for administrative decisions.
Mr Straw said: "Freedom of information is a fundamental part of that process and should significantly transform the relationship between citizens and the state."
A draft Bill is put out for widespread consultation, ahead of a move to bring in legislation. The Government came under pressure after the Queen's Speech when it emerged that no date was given for the publication of the draft.
There was some backbench concern that the Government, by only introducing a draft Bill, had put the manifesto pledge on hold after the sacking of Dr David Clark, the former cabinet office minister, last summer. Dr Clark was regarded as the leading campaigner for a Freedom of Information Act and had apparently already drafted legislation on the matter.
A Freedom of Information Act has been regarded as being at the heart of Tony Blair's pledge that New Labour had to be "whiter than white" after years of Tory sleaze.
Rhodri Morgan, the Public Administration Committee's chairman and a campaigner for freedom of information, said it was "very important" that after such a long delay the Bill was going to be published.
However, the key question remained how the Bill would define exceptions to the principle that information should be released, such as on the grounds that it would harm the national interest. Mr Morgan stressed it was vital that the Bill specified "substantial harm" as the test.