Bush made the announcement as authorities in New York and Washington moved to protect financial institutions from a supposed al-Qaida attack.
"We are a nation in danger. We're doing everything we can in our power to confront the danger," Bush said on Monday.
He appeared in the White House Rose Garden with top national security aides, and stopped short of recommending the new intelligence director be located in the executive office of the presidency, as the commission had recommended.
There have been bipartisan fears that putting the director in the White House could politicise the job.
Democrats accused Bush of dragging his feet on setting up the position nearly three years after the incidents occurred and not giving it sufficient spending authority to direct the operations of 15 agencies that gather intelligence.
"I think the fact that it's taken us three years to get here makes its own statement about urgency... We cannot afford reluctance in the protection of our country," Democratic presidential nominee John Kerry said.
Without real control of the intelligence budget, "that's a recipe for failure," said Representative Jane Harman, the top-ranking Democrat on the House Intelligence Committee.
"I think the fact that it's taken us three years to get here makes its own statement about urgency... We cannot afford reluctance in the protection of our country"
Democratic presidential nominee
White House Chief of Staff Andrew Card countered that the director would have "an awful lot of input into the development of any budgets in the intelligence community". Bush said the new director would coordinate the budget.
Bush, who initially opposed the establishment of the 11 September commission, is under political pressure in an election year to respond swiftly to the panel's recommendations.
Bush asked Congress to set up the position as part of an overhaul of the 1947 National Security Act that established the CIA and the National Security Council.
He also proposed setting up a national counter-terrorism centre to prepare a daily terrorism report for the president and act as the government's "knowledge bank" about terrorism.
Kerry, who has called for quick adoption of the commission's recommendations, said he believed the Bush administration's policies were encouraging recruitment of terrorists, a statement Bush said was a "ridiculous notion".
The White House acknowledged a "healthy debate" within the administration over creating what amounts to an intelligence czar and breaking with decades of giving agencies relative autonomy.
At least three members of Bush's national security team, such as Homeland Security Secretary Tom Ridge, had argued there was no need for a national intelligence director, saying it would create more bureaucratic layers.
But Bush said he opted for the new position "because I think it was the right thing to do". He said the panel investigating the absence of weapons of mass destruction in Iraq should consider whether the US government should establish a separate office to coordinate counter-proliferation efforts.
Bush agreed with the commission that Congress needed to reform its oversight of intelligence and homeland security.
John Kerry says Bush's policies
encourage 'terror' recruitment
"There are too many committees with overlapping jurisdiction, which wastes time and makes it difficult for meaningful oversight and reform," he said.
The commission report found that deep "institutional failings" by the US government led to the 11 September 2001 incidents.