Kib gave the strategic defence ministry to Osama Juili, commander of the Zintan fighters who on Saturday captured Seif al-Islam, the prominent son of slain dictator Muammar Gaddafi.
The interior ministry went to Fawzi Abdelal from the former rebel town of Misrata, whose fighters captured Gaddafi in October.
"I can reassure everyone: all of Libya is (represented) in the new government," Kib told a news conference in Tripoli as he unveiled the new line-up.
Other key appointments announced include Abdelrahman bin Yazza to head the oil and gas ministry and Ashur bin Khayyal as interim foreign minister.
Lawyer Fethi Tarbel, whose brief arrest on February 15 was the spark that set up a popular uprising against Gaddafi's regime in the eastern city of Benghazi, was named minister of youth and sport.
Tarbel later joined the NTC. NTC vice chairman and official spokesman Abdel Hafiz Ghoga said the new government had the confidence of the Libya's ruling body.