The pact will also set the stage for negotiations into a new security formula "to deter foreign aggression against Iraq" and to help Iraq fight "terrorism".
The two sides will work out how many of the current 160,000 US troops are to remain in Iraq and the legal framework under which they will operate, according to the White House.
Lieutenant-General Douglas Lute, the White House deputy national security adviser, said the size and shape of the long-term US presence in Iraq was a "key matter for negotiation".
"The two negotiating teams, Iraq and the United States, now have a common sheet of music with which to begin the negotiations," he said in Washington.
"Iraq is still under foreign occupation and Iraqis continue to die in great numbers"
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"The basic message here should be clear: Iraq is increasingly able to stand on its own, that's very good news, but it won't have to stand alone."
Lute said the bilateral agreements will not contain timetables for withdrawing US forces from Iraq, a move Bush continues to resist.
He added that it was important for neighbouring countries to know that the US considers Iraq a key factor in regional stability.
The US state department is to negotiate with the Iraqi side early next year.
On Monday, al-Maliki announced that he would ask the UN for a final renewal of its security mandate, stressing the importance of ending it in 2008.
"This is a goal pursued by all Iraqis who love their homeland and love it to be normal again without all the consequences it endured because of the policies and adventures of the previous [Saddam Hussein] regime," he said in central Baghdad.