The 193-member assembly approved Guterres by acclamation a week after the Security Council gave its own nod to his nomination.
He will succeed Ban Ki-moon, the South Korean whose second five-year term ends December 31.
Guterres, who was head of the UN's refugee agency for 10 years until 2015, had emerged as the Security Council's runaway favorite
after a series of straw polls.
Guterres will confront a range of issues, from war-torn Syria and Yemen to the acquisition of nuclear weapons by North Korea and the refugee crisis in Europe.
Samantha Powers, the United States' Ambassador to the UN, said last week that the recommendation of Guterres went smoothly because he was widely considered the most competent person for the job based on his experience, vision and versatility on a range of issues.
"It was remarkably uncontentious, uncontroversial, and I think it speaks to the fact that each of us represent our nation and each of us know how fundamentally important this position is in terms of the welfare of our own citizens," Powers said
after the Security Council's recommendation.
"If we have these transnational threats, and we don't have somebody at the helm of the United Nations that can mobilize coalitions, that can make the tools of this institution ... work better for people, that's going to be more pain and more suffering and more dysfunction than we can afford."
Guterres, a trained engineer who worked as an assistant professor before entering politics in 1974, led his country from 1995 to 2002 as head of the Socialist Party.
From 2005 to 2015, he served as the United Nations High Commissioner for Refugees. He is credited with cutting costs at the agency during his tenure, as well as lifting its performance as it grappled with the migrant crisis.
A practicing Catholic, Guterres remarried after his first wife died of cancer, and has two children.
In Guterres' vision statement in applying for the position, he wrote of the challenges facing the world in terms of rising inequality, terrorism and organized crime, climate change and the proliferation of armed actors internationally.
He wrote that the UN was "uniquely placed to connect the dots to overcome these challenges," but that change and reform are needed.
"People in need of protection are not getting enough," he wrote. "The most vulnerable, such as women and children, are an absolute priority. We must make sure that when someone sees the Blue Flag, she or he can say: 'I am protected'."