The announcement ends a stand-off between the Shiite alliance and Kurdish and Sunni parties opposed to outgoing Prime Minister Ibrahim al-Jaafari.
Mr Maliki now has 30 days to form a government.
Analysts believe he weill seek to form a national unity government with Shia, Sunni, Kurdish and secular politicians.
In his first policy speech, Mr Mali called for Iraq's militias to merge with the country's security forces.
US President George W. Bush said the nomination was a milestone on Iraq's path to democracy.
He hinted that the move may pave the way for the start of an American troop withdrawal.