Kurd Jalal Talabani has been re-elected president.
Maliki was appointed despite a dispute on Thursday evening that prompted about 60 members of Allawi's Iraqiya bloc to walk out during an acrimonious parliament session.
Before voting for a president, Iraqiya had called for three of its top members - barred for alleged ties to Saddam Hussein's Baath party - to be reinstated.
The support of Iraqiya, which narrowly won the 7 March poll and which gained most of its seats in Sunni areas, is seen as vital to preventing a resurgence of violence.
After being re-elected by MPs, Talabani named Maliki as the prime minister-elect. Maliki now has 30 days to form his cabinet, with the next parliamentary meeting scheduled for Saturday.