The veteran Libyan leader, elected chairman of the 53-nation AU at its annual summit last year despite opposition from some African leaders, said he would continue to push his dream of a fully integrated continent.
"There is no need for any title, I'll remain in the front struggling," Gaddafi said.
Al Jazeera's Amr El-Kahky, reporting from Addis Ababa, said: "Key players in Africa were reluctant to endorse the lobbying and the request of the Libyan leader to keep the chairmanship of the African Union for another year.
"He [Gaddafi] says he wants to complete what he has started - it's mission unaccomplished or unfinished business - but they told him behind closed doors that they are going to act according to the charter, which dictates the rotation of the chairmanship of the AU.
"That's why, within three minutes, Gaddafi has declared that he will hand over the presidency to Malawi."
"The resurgence of unconstitutional changes of government in Africa is a matter of serious concern"
Ban Ki-moon, UN secretary-general
In his acceptance speech, Mutharika said it was time for Africa to fulfill its promise, adding "the time has come for Africa to develop Africa".
"Africa is not a poor continent but the African populations are poor when we have actually a lot of natural resources," he said.
Earlier, the UN chief criticised power-grabs in Africa in a speech to the continent's leaders at the summit.
Ban expressed concern about a resurgence of "unconstitutional" power changes in Africa and rapped attempts by incumbents to change the law in order to continue in power.
"The resurgence of unconstitutional changes of government in Africa is a matter of serious concern," he said.
"We must also guard against the manipulation of established processes to retain power."
Africa has been dogged by political crises in the last year, including in Madagascar where Marc Ravalomanana was removed in an army-backed coup in March.'Succession structures'
In Guinea, the army seized power in December 2008 before massacring opposition followers in a football ground who protested against the coup.
Speculation that Gaddafi would seek another term was rife as the summit got under way and diplomats said he was likely to dominate talks, overshadowing scheduled discussions on the continent's conflicts.
However, Moses Wetangula, Kenya's foreign affairs minister, had maintained that "clear succession structures within the AU" would make it hard for Gaddafi to cling on.
"Every chairman serves one calendar year, unless there are serious extenuating circumstances, that would require continuation," he said.
Southern African Development Community (Sadc) presidents unanimously resolved that it is time Malawi, a southern Africa nation, assumed the leadership of the AU.
The Sadc heads of state nominated Mutharika at their regional summit in Kinshasa, Democratic Republic of Congo (DRC), in August 2009 to represent them during the elections of the AU chairman.