His inauguration marks a stunning comeback for the Marcos political dynasty, which was ousted after a popular revolt in 1986.
Mr Marcos Jr - nicknamed Bongbong - won an election landslide last month.
Sara Duterte, the daughter of the outgoing president, is being sworn in as vice-president.
Mr Marcos Jr took his oath of office at midday local time (0400GMT) in a colourful ceremony at the National Museum.
Flanked by his wife and three sons, he waved and smiled while observing a parade that featured an aerial display of jet fighters and march-pasts of Philippine's various uniformed personnel.
In his first speech as president, he thanked the crowd for delivering what he described as "the biggest electoral mandate in the history of Philippine democracy."