Sheikh Jaber Mubarak Al-Sabah, a senior member of the ruling Al-Sabah family, resigned on Monday as required by the constitution after Saturday's snap polls.
He should form the cabinet before December 11, when the new parliament is due to hold its inaugural session.
The Islamist-dominated opposition won nearly half the seats in the 50-member parliament and vowed to oppose the government's austerity measures in the face of low oil revenues.
The reappointment of Sheikh Jaber, 73, came despite calls by a number of opposition lawmakers to select a new premier to reflect the election results.
The official KUNA agency said the emir issued a decree reappointing Sheikh Jaber after consultations with former premiers and ex-parliament speaker Marzouk al-Ghanem.
Analysts expect the new parliament to have strained relations with the government.