The King has offered his thanks to the other Malay Rulers who had chosen him as the 15 Yang di-Pertuan Agong from Dec 13, 2016.
The king's role is largely ceremonial, as most of the authority to govern is held by the prime minister and cabinet.
The announcement on Sunday follows a leave of absence by the head of state and rumours he had married a former Russian beauty queen.
Despite mounting speculation in recent days the king might give up the throne, there was still palpable shock across the country at the first abdication of a king since the end of British rule in 1957.
"The Rulers have made a decision to hold a special Council of Rulers meeting on Thursday, 24th January 2019 for the goal of electing the Yang di-Pertuan Agong XVI (16) and the Deputy Yang di-Pertuan Agong".
The council comprises nine hereditary state rulers who take turns as Malaysia's king for five-year terms.
Malaysia's Conference of Rulers will convene on January 24 to choose a successor, who will be inaugurated on January 31, state news agency Bernama reported.
Malaysia's royal families have met to decide when a new king will be elected from among them after King Muhammad V unexpectedly resigned, according to the country's national news agency Bernama.
Reports then circulated online that he had married a former Miss Moscow in Russian Federation - although royal officials in Malaysia have so far not commented.
Sultan Muhammad V delayed Mahathir's swearing-in as prime minister after a historic election victory in May past year, and also delayed giving his consent to the appointment of a non-Muslim attorney general.
Sultan Muhammad V's resignation was in accordance with Article 32 (3) of the Federal Constitution, comptroller of the Royal Household Wan Ahmad Dahlan Ab Aziz said.
Local reports said it may take several weeks although Prime Minister Dr Mahathir Mohamad, whose Pakatan Harapan (Alliance of Hope) political pact unseated the decades-ruling Barisan Nasional coalition in a historic election defeat, said the government hoped Agong would be selected as soon as possible.
The palace has also said that the king is preparing to return home to the state of Kelantan.
A new monarch will now be elected by the Council of Rulers, according to the Straits Times.