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".
The president also pledged to be independent in exercising her custodial powers over the reserves, which are rarely tapped by the government.
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Halimah was a member of parliament for the ruling People's Action Party for nearly two decades before resigning to contest the presidency.
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.
But the absence of an election has angered Singaporeans, with many venting their ire on social media.
Social activist Gilbert Goh has organised 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.
"RIP! Democracy," wrote Mohamed Raizulee on Facebook.