Mr Mene, a South African native, was elected in February this year for the top job, beating three contenders.
He was sworn in at the headquarters in the African Union in Addis Ababa, witnessed by the president of the AU Commission and other officials.
He is a former Head of Mission to the World Trade Organisation for South Africa.
Ghana is hosting the Secretariat of the AfCFTA Secretariat.
The agreement initially requires members to remove tariffs from 90% of goods, allowing free access to commodities, goods, and services across the continent.