MCB will acquire 99.37 per cent of RBS Pakistan shares as part of the deal, with the option to purchase the remainder at a later date.
It will use internally-generated funds to pay for the acquisition, which will see it gain 75 branches in 24 cities across the country.
Chairman of MCB Mian Mohammad Mansha described the transaction as "important", noting: "It strengthens our franchise in the key urban centers and broadens our product offering to our retail as well as corporate customers."
His counterpart at RBS Pakistan Muhammad Aurangzeb added that the firm was "delighted" to reach an agreement with MCB, which he said will be an "excellent owner" of the franchise.
The move was confirmed to Reuters earlier this week by a source close to the deal, who told the news agency that the transaction would be valued at around $90 million.