The transaction could be closed in the first half of 2014 after approvals from the authorities and consent from the co-owner Budapest City Council.
A general meeting of MVM approved the acquisition on Dec. 17.
The National Asset Management Company (MNV) is committed to providing the necessary resources for the purchase, MVM said earlier.
A 50-percent-plus-one-share stake in Fogaz will remain in the hands of the local council of Budapest, MVM said.
Fogaz has 820,000 retail and corporate clients.