The increase in the budget takes US defence spending to levels not seen since the Cold War. Under Bush, the defence budget has risen from $330 billion in 2002.
"In this time of war, our military is facing greater sacrifice," Bush said on Monday as he signed the legislation in a ceremony at the Pentagon.
Since major combat operations were declared over on 1 May, 185 US soldiers have been killed by resistance fighters.
The American government has extended tours of duty in Iraq to 12 months and started planning for tens of thousands of regular and reserve troops to go to the war-ravaged country in 2004.
US defence spending dwarfs that of other countries. According to the latest available figures, Russia spends $65 billion, China $47 billion, Japan just over $42 billion and Britain more than $38 billion.
In addition to normal wages, the 2004 defence bill continues $225 per month in imminent danger pay and $250 in a monthly family separation allowance for troops in Iraq and Afghanistan.
"Your men and women in uniform are facing longer separations. Your families are feeling great pride and sometimes they worry," Bush said.
This defence budget will also allow the Air Force to buy 100 refuelling aircraft, expands veterans' benefits and will pay for research into new types of nuclear weapons.
It also includes $9.1 billion for ballistic missile defence and $12 billion for the purchase of Navy, Marine Corps and Air Force fighters.
But the president has come under criticism for not attending any funerals of soldiers killed in attacks in Iraq and for banning media coverage of the return of dead service members to the US.
Retired General Wesley Clark, a candidate for the Democrats' presidential nomination, has accused Bush of "the kind of cover-up tactics we saw during Vietnam".