The General National Congress confirmed the 42-year-old's appointment, making him Libya's youngest and fifth premier since long-time autocrat Moamer Kadhafi was toppled and killed in a 2011 uprising.
"Ahmed Omar Miitig was appointed head of the transitional government, and asked to form his cabinet and present it to the GNC for a confidence vote within 15 days," said the text of a decision signed by speaker Nuri Abu Sahmein.
A parliamentary deputy, Tahar al-Mokni, told AFP the decision to name the businessman as premier had been signed by Abu Sahmein, who was absent from Sunday night's session of the GNC to vote on his appointment.
The GNC indicated Abu Sahmein was abroad for unspecified treatment.
It is unclear if his decision to appoint Miitig will end a political and legal dispute over his election after it was rejected by several MPs and the deputy speaker, Ezzedine al-Awami.
Contacted by AFP on Monday, the spokesman for the outgoing government, Ahmed Lamine, was unable to comment on the GNC decision to appoint Miitig.
Since the 2011 uprising, successive governments in the oil-rich North African country have struggled to impose order as heavily armed former rebel brigades have carved out their own fiefdoms and refused to join the security forces.
Last month Zeidan's defence minister Abdullah al-Thani was appointed to replace him but stepped down after just five days, saying he and his family had come under attack.
State television broadcast footage from Sunday's chaotic session, the second in a week to decide between two candidates.
After an initial meeting on April 27, parliament gathered again on Tuesday, when Miitig won 67 votes in a first round with Benghazi university professor Omar al-Hassi second with 34 votes.
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