RNA - Halimah Yacob, a former speaker of parliament from the Malay Muslim minority, won the presidency in a walkover after authorities decided her rivals did not meet strict eligibility criteria.
While the role is largely ceremonial, the president has veto powers on key government appointments and safeguards the country's substantial financial reserves.
In her first speech as president, Halimah, 63, addressed the racial tensions that have sprung up as a result of the process and vowed to be president of all Singaporeans "regardless of race, language or religion".
"I look forward to the day when we will no longer need to... have reserved elections, and Singaporeans naturally and regularly elect citizens of all races as presidents," she added.
The president also pledged to be independent in exercising her custodial powers over the reserves, which are rarely tapped by the government.
Halimah was a member of parliament for the ruling People's Action Party for nearly two decades before resigning to contest the presidency.
Halimah Yacob making her first inspection of the Guard of Honor, with PM Lee Hsien Loong walking right behind her.
Authorities decided to allow only candidates from the Malay community to foster harmony in the city-state of 5.5 million people which is dominated by ethnic Chinese, and give more opportunities to minorities.
Halimah is the first Malay president of Singapore for almost five decades. The last was Yusof Ishak, president from 1965 to 1970, the first years of the city-state's independence.
But the absence of an election has angered Singaporeans, with many venting their ire on social media.
Social activist Gilbert Goh has organized a protest on Saturday at the city-state's designated free-speech corner.
"Our first-ever lady Muslim President Halimah will be inaugurated today and amid the pompous fanfare, Singaporeans feel a sense of betrayal that they have lost the chance to vote in the next head of state," he said in a statement ahead of the swearing-in ceremonies televised live.
Criticism of the electoral process continued to pour in on social media.
"RIP! Democracy," wrote Mohamed Raizulee on Facebook.