Quoting a close relative and member of parliament Simbaneuta Mudarikwa, NewsDay said the marriage ceremony was held privately at the 89-year-old President's rural home in the presence of close family members and friends, Xinhua reported.
Mugabe and Mudarikwa belong to the same political party Zanu-PF and were re-elected to their respective positions in the July 31 general elections.
Mudarikwa reportedly said a formal wedding ceremony would be held later.
"All went on well and we are all very excited as a family about this development," said Mudarikwa.
Mugabe has three young children, all with his second wife Grace. The youngest son was born when Mugabe was already in his 70s.
Bona graduated with a bachelor's degree in accountancy from City University of Hong Kong in 2011 and has been seen recently accompanying her father in public political events.