Ban Ki-moon will lead the UN for the next five years
The resolution, adopted unanimously, follows Mr Ban's nomination to succeed Kofi Annan by the UN Security Council.
Mr Annan is due to step down on 31 December after heading the UN for two five-year terms.
Mr Ban, 62, will be the first Asian to head the UN since Burma's U Thant, who held the post from 1961 to 1971.
The general assembly confirmed Mr Ban's appointment by acclamation - without a vote - on the basis of approval by all 192 members.
Priorities
Afterwards he told delegates he was "deeply honoured" and vowed to use his position to ensure that the organisation achieved more.
"The true measure of success for the UN is not how much we promise, but how much we deliver for those who need us most," Mr Ban said.
We reform not to please others, but because we value what this organisation stands for
Ban Ki-moon
Ban Ki-moon profile
Mr Ban cited poverty, HIV/Aids, environmental degradation, protecting human rights and combating terrorism among his priorities.
He also mentioned reforms - a key demand of the US, the UN's biggest contributor - but hinted that he would lead the process at his own pace.
"We reform not to please others, but because we value what this organisation stands for," he said.
"We cannot change everything at once. But if we choose wisely, and work together transparently, flexibly and honestly, progress in a few areas will lead to progress in a few more."
Mr Ban's appointment comes as the UN is trying to resolve the crisis over North Korea's nuclear programme.
He has played key roles in dealing with the standoff, both as South Korea's foreign minister and as its ambassador to the UN.
There was a broad consensus within the UN that the next secretary general should be Asian.
Mr Annan congratulated his successor, hailing him as "a man with a truly global mind" with "exceptional qualifications".
One of six candidates for the post, Mr Ban came top of all four informal polls in the Security Council and his five rivals all quit the race.
Ban Ki-moon
South Korean Ban Ki-moon, 68, has been endorsed unanimously by the  to succeed Kofi Annan as the  of the United Nations, on October 13. 

He will take the position of Secretary General on January 1.

When asked by   to adopt the resolution by an oral vote, the room filled with hundreds of diplomats and UN staff clapping loudly. A formal vote was not conducted as the decision was unanimous.

She banged her gavel after the vote and said, "It is so decided. I have the honor to announce that His Excellency Ban Ki-moon has been appointed by acclamation secretary-general of the United Nations. This is a historic day for the organization as it continues to evolve and live up to the values and principles of the ." 

At the time of the decision itself, the South Korean was the only candidate for the job - when informal polls were carried out within the UN, the other five individuals fared so badly that they all dropped out of the leadership race.

"I will work diligently to materialise our responsibility to protect the most vulnerable members of humanity and for the peaceful resolution of threats to international security and regional stability," Mr. Ban told the Assembly.

"The true measure of success for the UN is not how much we promise, but how much we deliver for those who need us most."

"The UN is needed now more than ever before."

Mr. Ban, the first Asian Secretary General since  from Burma, said he was committed to meeting , expanding peace operations and dealing with threats posed by terrorism and weapons of mass destruction, HIV/AIDS and other pandemics, environmental degradation and protecting human rights.

He also mentioned , something the United States — which contributes the largest part of the budget of the UN, with 22 % , but also has arrears of 1.3 billion dollars — has long called for. However, the new Secretary General made clear that any changes would occur at his own pace.

"We reform not to please others, but because we value what this organisation stands for," he said. 

"We cannot change everything at once. But if we choose wisely, and work together transparently, flexibly and honestly, progress in a few areas will lead to progress in a few more." 

Kofi Annan, 68, described Ban as "a future secretary-general who is exceptionally attuned to the sensitivities of countries and constituencies in every continent. A man with a truly global mind at the helm of the world's only universal organisation."

He added that he wished Ban strength and courage as he prepared to take over the job and to "have fun along the way."

"We believe he is the right person to lead the United Nations at this decisive moment in its history, particularly as the UN struggles to fulfill the terms of the reform agenda that world leaders agreed to last fall," U.S. Ambassador John R. Bolton told the assembly.

Israeli Ambassador Danny Gillerman said that it was good for Israel's standing in the organization.

"If the secretary general is serious and fair and appoints underlings who are serious and fair, and the UN will be serious, clean and organized, this will be good for the Jews,"  said Mr. Gillerman.

Mr Ban will hold the position for five years until the next election in 2011.