UNITED NATIONS—The U.N. General Assembly on Thursday officially appointed António Guterres of Portugal as its next secretary-general as he pledged to combat terrorism and extremism while also fighting “xenophobia” and populism.

The 193-member General Assembly voted by acclamation after the Security Council last week nominated Mr. Guterres for the post following straw polls that showed him leading a dozen other candidates.

Mr. Guterres, 67, said he felt “a profound sense of responsibility” and that he would serve all member states without an agenda.

In his first address to the U.N. as the Secretary-General designate, Mr. Guterres acknowledged the challenges he would face, resolving such conflicts as Syria and addressing gender equality, as well as the limitations that come with the position.

“We must make sure that we are able to break these alliances between all those terrorist groups or violent extremists on one side, and the expression of populism and xenophobia on the other side,” he said. “We must be able to fight both of them with determination.”

He added that he would not have all the answers and would not seek to impose his own views.

His approach would be “one in which the secretary-general makes his good offices available, working as a convener, a mediator, a bridge-builder and an honest broker to help find solutions that benefit everyone involved.”

Mr. Guterres is a seasoned politician and a veteran of the U.N. He served as Portugal’s prime minster from 1995 to 2002, gaining a reputation as an ethical leader willing to reach consensus with his critics. At the U.N., Mr. Guterres served as the world body’s high commissioner for refugees from 2005 to 2015, often traveling to conflict zones and border areas to advocate for the plight of refugees.

The General Assembly broke into long applause Thursday as diplomats gave Mr. Guterres a standing ovation. Representatives from different regions of the world delivered statements of congratulations and well wishes, and outgoing Secretary-General Ban Ki-moon described him as someone best known “on the front lines of armed conflict and humanitarian suffering.”

Diplomats also praised the new, more transparent process under which Mr. Guterres was selected and said they hoped that this signaled an era of change in the wider U.N. system. Until this year, the Security Council picked the secretary-general in secret consultations and without any input from member states.

“Mr. Guterres has the character, vision, and skills needed to lead the United Nations at this critical moment and to reform its organizations and operations to better meet these unprecedented challenges,” President Barack Obama said in a statement.

Mr. Guterres is due to hold a session with the General Assembly next week and the process of transition has been set in motion. Mr. Guterres will appoint a deputy and new team for senior U.N. positions to head various agencies from peacekeeping to humanitarian relief and political affairs.