"On this occassion, I call upon our brother Jawad al-Maliki to form the next Iraqi government," said Talabani, who was himself re-elected as Iraqi president during Saturday's parliamentary session in Baghdad.
The parliament also voted to give Mahmoud al-Mashhadani, a Sunni Arab, the position of speaker.
Al-Mashhadani's two deputies are to be Khalid al-Attiyah, a Shia, and Aref Tayfour, a Kurd.
The move ends four months of political deadlock during which sectarian tensions had threatened to spill over into full-scale civil war.
In his first speech as prime minister-designate, al-Maliki said armed militias should merge with government forces.
"Arms should be in the hands of the government. There is a law that calls for the merging of militias with the armed forces," he said.
Al-Maliki was nominated by the Shia alliance after Sunnis and Kurds rejected the candidacy of his close ally and previous prime minister, Ibrahim al-Jaafari.
He is a leading figure in al-Jaafari's Dawa party and has often appeared as his spokesman.
Sunni and Kurdish politicians blamed al-Jaafari for the rise in sectarian tensions in Iraq and for failing to rein in Shia militia's working alongside the interior ministry.
The Shia alliance won the largest number of seats at the country's December elections but needed the support of Sunni and Kurdish politicians to form a national unity government.