The president welcomed the move, which allows him to use force against Baghdad if the United Nations fails to disarm Iraq.
Following the House's 296-133 vote in favour, the Senate is expected to endorse the step on Friday.
America's staunchest ally, UK Prime Minister Tony Blair, is currently in Russia, where he is trying to garner support for a tougher UN Security Council resolution on Iraq.
'Clear message'
The president and his supporters have spent several days lobbying Congress to support the resolution.
The text authorises the president to use force against Iraq in a manner "necessary and appropriate" to protect US national security and enforce UN resolutions.
However, the resolution encourages Mr Bush to pursue all diplomatic means before he decides on any attack.
It calls on him to certify to Congress - either before a military strike or very shortly afterwards - that diplomatic and other peaceful means have failed.
It also stipulates that he reports to Congress every 60 days if he does take action.
President Bush said the resolution sent "a clear message to the Iraqi regime".
"It must comply or it will be forced to comply. The days of Iraq acting as an outlaw state are coming to an end," he said.
Retaliation fear
The move comes amid a growing row over whether or not America's foreign intelligence agency, the CIA, genuinely believes that Saddam Hussein poses an immediate threat.
Before the vote, the BBC's correspondent in Washington, Justin Webb, said some Democrats had been planning to vote no.
They point to a recently declassified letter from the CIA director, George Tenet, to a congressional committee in which he appeared to cast doubt on the immediacy of the threat from Saddam Hussein.
Mr Tenet said the Iraqi leader seemed to be drawing a line short of mounting terrorist attacks on the United States.
The letter added that there was a risk of Saddam Hussein using weapons of mass destruction in response to an American strike.
One Democrat congressman said President Bush was risking triggering the very thing he was trying to prevent - the use of these weapons.
In a latest round of diplomacy, UK Prime Minister Tony Blair has arrived in Russia to try to gain support for a new UN resolution compelling Iraq to disarm.
Russia - which has a veto in the Security Council - has so far resisted US and UK calls for a new resolution which would include the threat of force against Iraq.