It said the deal will "significantly enhance" its presence and growth opportunities "within a fast-growing and attractive market".
BOG said the Armenian market has similar characteristics to Georgia, and pointed to significant upside potential from leveraging the group's existing customer focus and digital/payments capabilities.
Mel Carvill, chairman of the board of directors of Bank of Georgia, said: "This transaction is a significant milestone for the group and a new chapter in our strategic development. Through Ameriabank we are set to enter Armenia, one of the fastest-growing economies in the region. Ameriabank has a well-regarded and experienced management team, and I am delighted that they will stay on after the transaction is closed.
"The board believes this transaction will enable the group to substantially increase scale and unlock additional growth opportunities as our impressive results in digitalisation, payments and customer franchise growth can be applied to Ameriabank's further development. This transaction is immediately earnings enhancing, using the group's existing cash resources, with no dilution for existing shareholders. The board unanimously views it as an excellent opportunity to create more value for our shareholders."