At his inaugural speech he promised to make sweeping changes to the country`s political system.
"I see the erosion of the people`s trust in their country`s leaders," he said.
"The erosion of faith in our judicial system. The erosion of confidence in the capacity of our public servants to make the people`s lives better, safer and healthier."
Nicknamed "The Punisher", Mr Duterte is credited with a dramatic reduction in crime in Davao, but rights groups say it was at the expense of human rights.
He has also promised to end corruption and spread wealth around the country.
Mr Duterte, who has barely left the Davao in the south since his election win, took his oath at a small ceremony at the Malacanang Palace in Manila.
Only state media were permitted to cover the event.
Under the constitution, he and his vice-president, Leni Robredo, will both serve a single six-year term.
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