His mother, Corazon, won the Philippines presidency after leading the 1986 "people power" revolution that toppled Marcos.
Much of the crowd attending Wednesday's inauguration ceremony was dressed in yellow, the colour associated with the people power movement.
"I was here 24 years ago for his mother's political rally and I came here to see Noynoy take his oath because I want him to succeed," supporter Sonia de la Cruz told Reuters.
"I will pray for him. I hope he stops people in government from stealing and delivers his promises to us"
Sonia de la Cruz,
"I will pray for him. I hope he stops people in government from stealing and delivers his promises to us."
Al Jazeera's Marga Ortigas, reporting from Manila, said many Filipinos have high expectations of the new president.
"Many are hoping that important and effective decisions will be made by Aquino that will go toward alleviating poverty and ending the armed unrest in parts of the country," she said.
"But it is still early days and there is a sense of understanding that it will take a while for Aquino to achieve this."
On Tuesday, Aquino implemented his first task as president by naming a new cabinet.
He also announced plans to immediately form a "Truth Commission" aimed at investigating allegations of corruption and human rights abuses under the administration of his predecessor, Gloria Macapagal Arroyo.
|Aquino accuses Arroyo of massive graft during her term as president [Reuters]
Officials who committed "crimes against the people will be made to pay," he said at a news conference on Tuesday.
Arroyo has repeatedly denied any wrongdoing.
In his inauguration speech Aquino made several stinging criticisms of his predecessor, labelling Arroyo's presidency a "regime indifferent to the appeals of the people".
On Tuesday Aquino also introduced his cabinet, which included loyal supporters and former cabinet members of Arroyo's government.
He named retired General Voltaire Gazmin as his defence secretary, who had previously headed the elite force that protected his mother and defended her government against at least seven coup attempts.
Foreign secretary Alberto Romulo was the only Arroyo cabinet member to retain his post.
A close Arroyo associate, Romulo surprised many when he announced his support for Aquino before the May 10 elections.
Aquino, a 50-year-old economics graduate, said he will temporarily lead the Department of Interior and Local Governments, which controls the national police and local officials.
After promising to eradicate poverty during the election campaign, Aquino has been careful to play down expectations, insisting that he is not Superman and that he is hoping to merely lay a solid foundation for his successor in 2016.
The Philippines has been grappling with poverty, corruption, armed conflicts and deep social divisions for decades.
A third of the population lives on a dollar a day, and about 3,000 Filipinos leave daily for jobs abroad.
Aquino has also expressed alarm at the ballooning national budget deficit, which he said could surpass $8.7bn this year.