The 90-year-old was elected by his fellow heads of state to replace Mauritania's Mohammed Ould Abdel Aziz in the role, which rotates between the continent's five regions.
"By electing me to preside over this august body, with full knowledge of the onerous responsibility that lies ahead, I humbly accept your collective decision," Mugabe said as he was appointed at the AU summit in Addis Ababa, Ethiopia.
Africa's longest-serving leader is still viewed with respect by many on the continent after he led Zimbabwe to independence, however, he is subject to travel bans in the European Union and US.
He was given a rare invitation to an EU-Africa summit in Brussels last year, but boycotted it after his wife was refused a visa.
When he initially took power he was seen as promoting reconciliation, but controversial land reforms that forced out white farmers from 2000 onwards drew ire in the West.
Since then, he has increasingly been accused of human rights abuses and vote-rigging as his ZANU-PF party has clung on to power.
- Sky News