Al-Zurfi has 30 days to form his cabinet which he must then put to a vote of confidence in Iraq's fractious parliament.
The 54-year-old former governor of the holy Shiite city of Najaf heads the Nasr parliamentary grouping of former prime minister Haider al-Abadi, Al Jazeera reported.
He would replace caretaker Prime Minister Adel Abdul Mahdi, who quit in December following demonstrations against a government that protesters say has failed to provide them with economic opportunities and basic services.
Al-Zurfi's appointment came two weeks after former prime minister-designate Mohammed Allawi withdrew his candidacy for the post, accusing political parties of obstructing him.