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The vote seals the United Nations' 15 January deadline for the Iraqi President, Saddam Hussein, to order his troops out of Kuwait, or face military action.
After three days of sometimes heated debate, the House of Representatives passed the motion authorising use of force by 250 votes to 183.
The Democrat-controlled Senate vote was far closer, at 52 to 47, but was not as narrow as had been feared.
It is the first time Congress has approved military action since the Gulf of Tonkin resolution in 1964 at the start of the Vietnam War, and it was by no means a foregone conclusion.
At times the Senate vote was too close to call, and some were predicting the president would be forced to go to war without Congressional backing.
The House of Representatives added one condition to the motion: that all diplomatic and peaceful means of averting war should be exhausted.
It has also made it clear it will withdraw its support if the war becomes prolonged or results in heavy casualties.
President Bush welcomed the votes, saying they represented the "last best chance for peace" and sent "the clearest message to Iraq that it cannot scorn the January 15 deadline".
He said he had not yet made a final decision to launch an attack on Iraq, but warned it would be "sooner rather than later" if Saddam Hussein did not withdraw.
Senior Washington sources said the president had obtained permission from the British, Saudi Arabian and Egyptian governments to launch an attack at only a few minutes' notice.
The tough line was reinforced by the British foreign secretary, Douglas Hurd, in Abu Dhabi on a trip to the Gulf.
"He [Saddam] will be forced out," he said. "We are coming to a decision on this. There is no reason for a long delay."
In a last-minute effort to avert war with diplomacy, the UN Secretary-General, Javier Perez de Cuellar, arrived in the Iraqi capital Baghdad yesterday with his latest five-point peace plan endorsed by EC foreign ministers.
He met Tariq Aziz, the Iraqi Foreign Minister, this evening and is due to meet Saddam Hussein tomorrow. However, although Washington publicly supports his efforts, all preparations are for imminent war.
The last-minute diplomacy by Perez de Cuellar and others came to nothing.
Iraq continued to refuse to comply with the UN ultimatum for its troops to withdraw from Kuwait, and at 2330 GMT on 16 January 1991, Operation Desert Storm began with a devastating aerial bombardment of Baghdad.
After more than a month of intensive air attacks, the Allies began a land offensive on 24 February. One day later, the Iraqi army began retreating.
On 28 February, President George Bush declared victory.
Kuwait was liberated, but the Gulf War left Saddam Hussein in power.
The US and Britain launched a second war against Iraq in 2003. Saddam Hussein was overthrown and captured. He was later tried for war crimes by an Iraqi court, sentenced to death and executed.
A democratically-elected government was sworn in after elections in 2005.
However, it has proved very difficult to find an acceptable balance of power between Iraq's national groups, and the country continues to be destabilised by violent extremists.
American and British troops have so far been unable to pull out despite repeated guerrilla attacks which have killed more soldiers than the war itself.
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