Mr Guterres, 67, will become the world’s top diplomat on 1 January when Ban Ki-moon’s second five-year term ends.
The Portuguese, who led the UN refugee agency UNHCR for 10 years, was chosen from among 13 candidates last week.
He said he would fulfil his role with gratitude and humility.
Mr Guterres, who trained as an engineer, entered politics in 1976 in Portugal’s first democratic election after the "Carnation revolution" that ended five decades of dictatorship.
As head of the UNHCR refugee agency from 2005 to 2015, he led the agency through some of the world’s worst refugee crises, including those in Syria, Afghanistan, and Iraq.
During that time, he repeatedly appealed to Western states to do more to help refugees fleeing the conflicts.
Mr Guterres’ nomination came despite a concerted effort to appoint the UN’s first female secretary general. Of the 13 candidates, seven were women, among them Unesco director general Irina Bokova, from Bulgaria, and Helen Clark, 66, a former prime minister of New Zealand and current head of the UN development programme.
Mr Guterres told the assembly: "The dramatic problems of today’s complex world can only inspire a humble approach. One in which the secretary general alone neither has all the answers, nor seeks to impose his views.
"One in which the secretary general makes his good offices available, working as a convenor, a mediator, a bridge-builder and an honest broker to help find the solutions that benefit everyone involved."
Mr Ban told the assembly that his successor was well-known in diplomatic circles as a man of compassion.
"He is perhaps best known where it counts most - on the frontlines of armed conflict and humanitarian suffering," Mr Ban said.
"His political instincts are those of the United Nations - co-operation for the common good and shared responsibility for people and the planet."