The testimony of Lewis "Scooter" Libby, Vice-President Dick Cheney's former chief of staff, according to court papers made public on Thursday, links Bush directly to the leak for the first time.
The revelation could be politically damaging for the US president who has frequently denounced leaks from his administration and vowed to punish those responsible.
Libby testified to a federal grand jury that Cheney had told him that Bush authorised him to disclose information from a secret national intelligence document to a New York Times reporter in July 2003.
The disclosure arose out of a long-running investigation into the leak of CIA operative Valerie Plame's identity.
Directed by Cheney
Libby testified that he was specifically directed by the vice-president to reveal intelligence information to the then New York Times reporter Judith Miller.
The court documents did not say that Bush or Cheney authorised Libby to disclose Plame's identity.
Libby also said he was cleared to brief the reporter about Plame's husband, Joseph Wilson, a former ambassador who had criticised Bush's decision to invade Iraq in 2003.
Bush ignored a reporter's shouted question about the case and the White House declined to discuss the disclosure.
"Our policy is not to discuss ongoing legal proceedings and that policy is unchanged," said spokesman Ken Lisaius.
"The president has said he'd fire anyone who leaked this kind of information. But it now seems that he authorised leaks just like this in the first place"
New York Democratic senator
Libby resigned from the administration last October when he was charged with perjury and obstruction of justice by special prosecutor Patrick Fitzgerald, who is investigating the leaking of Plame's name.
The information about Bush came to light in a 39-page document filed by Fitzgerald in which he argued against Libby's demand for more government documents, which his lawyers say he needs to defend himself.
Libby testified he had been authorised to disclose the information because it rebutted Wilson and Cheney thought it "very important" for it to come out.
Wilson has said White House officials deliberately leaked his wife's identity to pay him back for attacking the grounds used by Bush to justify the Iraq invasion.
Bush had the authority to declassify the material. But the court papers quoted Libby as saying that "it was unique, in his recollection" to get approval from the president, via the vice-president, for such an action.
The leak occurred at a time when opponents were stepping up their criticism of the March 2003 invasion after US forces had failed to find weapons of mass destruction in Iraq.
Libby said he brought a brief summary of the key findings when he met Miller on July 8, 2003 at a hotel.
Bush has previously promised to
punish those behind leaks
Democrats demanded an explanation.
In Congress, Harry Reid, the Senate Democratic leader, said: "President Bush must fully disclose his participation in the selective leaking of classified information."
Charles Schumer, another Democrat, said: "The president has said he'd fire anyone who leaked this kind of information. But it now seems that he authorised leaks just like this in the first place. The American people deserve the truth."
Bush has often complained about leaks in Washington and has vowed to take action against those who released unauthorised information to the public.
"There are too many leaks of classified information in Washington," he said after the Plame news broke in 2003.
"There's leaks at the executive branch, there's leaks in the legislative branch. There's just too many leaks. And if there is a leak out of my administration, I want to know who it is," he had said then.