Antonio Guterres beat 12 other candidates, seven of them women, to be sworn in as the ninth United Nations secretary-general.
The former Portuguese prime minister placed his hand on a copy of the UN Charter in front of the 193-member General Assembly as he took the oath.
The 67 year-old pledged to personally help broker peace in various conflicts and to reform the United Nations to become more effective.
He says there is fear around the world and it must be dealt with.
"Fear is driving the decisions of many people around the world. And we must understand their anxieties and meet their needs without losing sight of our universal values. It is time to reconstruct relations between people and leaders, national and international."
Mr Guterres will replace Ban Ki-moon, of South Korea, on January the 1st.
Ban Ki-moon steps down after serving two five-year terms.
The president of the UN General Assembly, Peter Thomson, says his service will not be forgotten.
"For 10 years, Secretary-General Ban was an unrelenting force in raising global awareness of the catastrophic consequences of our planet's warming and in galvanising world leaders to act. On behalf of the General Assembly, I offer profound thanks to Secretary-General Ban Ki-moon for his service to the United Nations."
Mr Guterres is the first former head of government to be elected to run the global organisation.
He was prime minister of Portugal from 1995 to 2002, then was the UN High Commissioner for Refugees from 2005 to 2015.
Diplomats are now watching to see who Mr Guterres appoints to senior UN positions.
He is expected to name Nigeria's environment minister, Amina Mohammed, as his deputy secretary-general and to appoint a woman as his chief of staff.
Diplomats and officials have speculated China would like one of its people to head peacekeeping and Russia is keen to have a senior role.
Mr Guterres reportedly is looking for a big shake up of the organisation and would like to create a form of cabinet to run a more collective leadership.
The departing Ban Ki-moon says it is important the United Nations continues to do all it can to promote world peace.
"I have maintained a focus on people's dignity and rights, the pillars of our common humanity. I have sought to stand up for the vulnerable and those left behind today. And I have tried to be sure that we are doing all we can so that future generations can live in peace. Shukran jazeelan, xiexie, thank you very much, merci beaucoup, spasibo bolshoe, muchas gracias, thank you."
