President Tony Tan Keng Yam and Prime Minister Lee Hsien Loong have written congratulatory letters to Malaysia's 15th king, Sultan Muhammad V.
The King took the oath of office in the Istana Negara, or national palace, in Kuala Lumpur, on Dec 13.
Sultan Muhammad V, currently the ceremonial ruler of the conservative Islamic northern state of Kelantan, takes the national throne under the rotating monarchy that has been in place since the country's independence from Britain in 1957.
In a unique arrangement, the throne of the Muslim-majority country changes hands every five years between the rulers of the nine Malaysian states still headed by Islamic royalty.
In his letter, Dr Tan said: "On behalf of the people of Singapore, I extend my warmest congratulations on the historic occasion of Your Majesty's assumption of office as the Fifteenth Yang di-Pertuan Agong of Malaysia.
"I am confident that Malaysia under Your Majesty's guidance will continue to develop and prosper. The relations between Malaysia and Singapore are deep and multi-faceted, and the two countries share many common interests. I look forward to working with Your Majesty to strengthen these relations.
"My wife and I offer our best wishes for Your Majesty's good health, happiness, and success."
Mr Lee said in his letter: "On behalf of the Government of Singapore, I would like to extend my warmest congratulations on the occasion of Your Majesty's assumption of office as the Fifteenth Yang di-Pertuan Agong of Malaysia.
"I am confident that Malaysia will enjoy good progress during Your Majesty's reign. We deeply appreciated Your Majesty's attendance at the lying-in-state of the late Mr Lee Kuan Yew in March 2015.
"Malaysia and Singapore share a long history built on close people-to-people ties. Looking forward, joint projects like the Kuala Lumpur-Singapore High-Speed Rail will bring the peoples of Malaysia and Singapore even closer together. I hope to deepen the relationship between our countries during Your Majesty's reign.
"My wife joins me in wishing Your Majesty every success."