The Ghanaian-born Annan, 68, ends his term at the end of the month, and will be replaced by South Korean Ban Ki-moon Jan. 1.
The body unanimously adopted a resolution of tribute for Annan, whom the assembly's president, Sheikha Haya Rashed Al Khalifa of Bahrain said had devoted his life to the organization.
"He has risen through the ranks of the United Nations and devoted his life's service to the organization," Sheikha Haya said. "So, today we are not only bidding farewell to the current Secretary-General, but also to one of the longest-serving officials of the United Nations."
Annan said while there had been setbacks, he was proud of the agency's progress during his tenure.
"I depart convinced that today's United Nations does more than ever before, and does it better than ever before," Annan said. "Yet our work is far from complete -- indeed, it never will be."