Goodman claims in the letter addressed to the human resource director at the Sunday newspaper's parent company that phone hacking was carried out with "the full knowledge and support" of the paper's leadership.
The claim is particularly damning because both News of the World and parent company News International have long insisted that Goodman - who was fired, convicted and jailed for his role in the scandal - was the only reporter involved in intercepting voicemail messages.
Goodman's letter, addressed to Daniel Cloke and dated March 2, 2007, directly contradicts that.
Goodman said he was acting with the backing of senior journalists, that other staff at the News of the World were also hacking phones, and that "this practice was widely discussed in the daily editorial conference, until explicit reference to it was banned by the editor."
The names of those involved have been obscured in the letter. The Guardian newspaper, which first published the correspondence, said this was done by police, who are investigating wrongdoing at the newspaper.
The letter is among a batch of documents published by the House of Commons' culture, media and sport committee.
Ahead of the publication, members committee said they were likely to recall James Murdoch to answer more questions about phone hacking at the News of the World. Murdoch, who runs the European division of his father Rupert's media empire, testified last month that he was unaware of evidence of widespread phone hacking at the newspaper.
His testimony was disputed two days later by former News of the World editor Colin Myler and ex-company lawyer Tom Crone.
Members of the Culture, Media and Sport committee said they have not managed to reconcile the contradictions between those statements. Committee Chief John Whittingdale said it "may wish to put further questions to James Murdoch."
He also said Myler and Crone would give evidence to the lawmakers next month. Committee member Tom Watson said "it is likely we will take Murdoch back."
"There seems to be a question as to whether James Murdoch himself misled the committee," Watson said. "We have not reached a conclusion on that."
Whittingdale said there are no plans to recall Rupert Murdoch, who gave evidence to the committee alongside his son on July 19.
Police are investigating claims the News of the World illegally accessed cell phone messages and bribed police to get information on celebrities, politicians and crime victims.
News International said Tuesday it is "cooperating fully" with the police investigation.
"We recognize the seriousness of materials disclosed to the police and Parliament and are committed to working in a constructive and open way with all the relevant authorities," it said in a statement Tuesday.
Rupert Murdoch's News Corp. shut down the 168-year-old newspaper last month.