The money will be used to upgrade equipment for US troops and accelerate efforts to train and equip Iraqi forces, Bush said on Tuesday.
The $80 billion request will push funding for military operations in Iraq and Afghanistan to a record $105 billion for fiscal year 2005 alone, including $25 billion in emergency spending already approved.
The new money will supplement the Pentagon budget, which already totals more than $400 billion.
Military operation in Iraq already cost more than $1 billion a week.
The request for the additional funding will be submitted to US Congress early next month and is expected to be approved despite lawmakers' concerns about record federal budget deficits and complaints that Bush and his top advisers initially underestimated the costs.
Before the invasion, then-White House budget director Mitch Daniels predicted Iraq would be "an affordable endeavour" and Deputy Defence Secretary Paul Wolfowitz assured Congress: "We are dealing with a country that can really finance its own reconstruction and relatively soon."
The war is proving costly, both in
terms of money and lives
When then-White House economic adviser Lawrence Lindsey estimated Iraq would cost $100 billion to $200 billion, he was derided by administration colleagues and later lost his job.
A senior administration official said the announcement for fresh funding, before Sunday's election in Iraq, should signal to the new government that "we will support that government in their efforts to acquire the wherewithal to be able to provide for their own security".
Nearly the entire package - $75 billion – will fund military operations, mostly for a force of 150,000 US soldiers, Marines and other troops in Iraq.
Additional money will be included to upgrade Army equipment, addressing concerns about a shortage of armour for vehicles.
The US Army plans to keep at least 120,000 troops in Iraq for the next two years to train and fight alongside Iraqi forces.
In addition, at least $780 million would go to combat the drug trade in Afghanistan, congressional aides said.
Not including the new funding request, Congress has approved $120 billion for Iraq and $60 billion for Afghanistan. Last year, it also approved a $25 billion contingency fund for the Pentagon.