The 185-member General Assembly ratified the 58-year-old Ghanaian by acclamation as successor to Boutros Boutros-Ghali of Egypt, who was vetoed for a second term by the United States. Washington claimed he was sluggish in pressing cost-cutting reform. Mr Annan, who was chosen last Friday by the 15-member Security Council, took his oath of office, although his five-year term does not begin until 1 January.
The General Assembly also thanked Mr Boutros-Ghali, who received a standing ovation after a farewell speech in which he blamed member states, including Washington, for the financial crisis, which has slowed UN reform.
Mindful of Washington's demand for reform, Mr Annan urged the UN to "make change our ally, not our enemy".
The head of UN peace-keeping was chosen by the Security Council after France backed down in its opposition, in part because he was a US favourite.
Mr Annan promised also to lead a UN staff "that will be honest, efficient, independent and proud of its contribution to the improvement of life on this planet."