His rise to power, 36 years after an army-backed "People Power" revolt booted his father to global infamy, upends politics in the Asian democracy, where a public holiday, monuments and the Philippine constitution stand as reminders of his father's tyrannical rule.
Activists and survivors of the martial law-era under his father protested Marcos Jr's inauguration, which took place at noon on Thursday at the steps of the National Museum in Manila.
Chinese Vice-President Wang Qishan and US Vice-President Kamala Harris's husband, Doug Emhoff, were among foreign dignitaries attending.
Marcos Jr received more than 31 million votes and Sara Duterte more than 32 million of the more than 55 million votes cast in the May 9 election.
The massive victories will provide them robust political capital as they face tremendous challenges as well as doubts arising from their fathers' reputations. It was the first majority presidential victory in the Philippines in decades.
Outgoing president Rodrigo Duterte presided over a brutal anti-drugs campaign that left thousands of mostly poor suspects dead in an unprecedented scale of killings the International Criminal Court was investigating as a possible crime against humanity.
The probe was suspended in November, but the ICC chief prosecutor has asked that it be resumed immediately.
Marcos Jr, a former governor, congressman and senator, has refused to acknowledge or apologise for massive human rights violations and plunder under his father's rule and has defended his legacy.
During the campaign, he and Sara Duterte avoided controversial issues and focused on a call for national unity, although their fathers' presidencies opened some of the most volatile divisions in the country's history.
Marcos Jr appealed to be judged "not by my ancestors, but by my actions".
His father was forced from power by a largely peaceful pro-democracy uprising in 1986 and died in 1989 while in exile in Hawaii without admitting any wrongdoing, including accusations that he, his family and cronies amassed an estimated $US5 billion to $US10 billion while in office.
