Announcing his resignation in the National Assembly two months after assuming the job, Hussain said Aziz would be taking over the top post shortly.
Aziz, currently the Finance Minister had been hand-picked by President Pervez Musharraf after the sudden resignation of Zafarullah Khan Jamali in June. However, he could not take over the post directly as he was not a member of the National Assembly.
Hussain, a Musharraf loyalist and President of the ruling Pakistan Muslim League-Q, (PML-Q), was appointed interim Prime Minister until Aziz was elected to the lower house.
Aziz, who recently escaped a suicide bomb attack, was elected last week from two constituencies, and will now become Pakistan's 20th Prime Minister on August 27.
