The House voted 388-43 for the bill that includes a measure rejecting Bush's plan to use part of the money to build an embassy in Iraq, potentially delaying construction.
"The bill involves sizable amounts of money designed essentially to support our troops wherever they may be but especially in the Middle East," said House Appropriations Committee chairman Jerry Lewis, a California Republican.
The Senate must approve its version of the bill and then the two chambers will have to work out differences before it can become law. The Senate is expected to start work on it next month.
"I thank the House for its quick action and look forward to working with the Senate so that all of my top priorities are included in the final legislation," Bush said in a statement.
If approved, the bill would bring to almost $300 billion the amount Congress has authorised in emergency war spending since US-led forces invaded Iraq in March 2003.
The bulk of the funds - $77 billion - would cover defence costs to help pay for the wars in Iraq and Afghanistan. That money, $1.8 billion more than Bush asked for, would be used to buy new weapons, body armour and medical supplies for troops.
Democrats largely supported the Republican-written bill but said Congress was not providing enough oversight of how the money was being spent.
The bill particularly provides for
US troops in the Middle East
They cited a military audit released on Monday that said leading US defence contractor Halliburton, once headed by Vice-President Dick Cheney, may have overcharged the US
government by more than $100 million under a no-bid oil deal in Iraq.
Republican lawmakers who wrote the bill have had to balance spending pressures with a request by Bush and some conservative Republicans for fiscal discipline to bring down the record budget deficit.
In an effort to cut costs, the House measure bars the White House from using $592 million in the bill to build a Baghdad embassy.
The bill cuts $400 million Bush had asked for to reward war allies. In a statement, the White House asked the House to put it back, saying it would help partners such as Poland and Slovakia.
Lawmakers also left out $570 million the president requested for reconstruction projects in Afghanistan and chopped $66 million for counter-narcotics projects. The bill provides $594 million for anti-drug programmes and police training in that country.
The bill additionally cuts $45 million Bush asked for to pay for US participation in an international debt relief plan for countries hit by the Asian tsunami. The bill left intact $656 million in tsunami disaster relief.