The $225 million deal will see Amro acquire Prime's 69 branches throughout Pakistan and become the second-largest foreign-owned bank in Pakistan.
Amro has also announced it is to bid for the remaining shares from minority stockholders.
It is thought that Prime's appeal to Amro lies in the fact that over half of its loan portfolio is with small-to-medium businesses, which represents a chance for the Dutch bank to diversify its risk portfolio in the fast-growing sector.
Moreover, the bank's outlets will bring Amro's total in Pakistan to 80 and thus enable them to establish an increased presence in a retail banking market that remains relatively untapped.
Commenting on the acquisition, Jeroen Drost of Amro said: "Pakistan has one of the world's fastest growing financial markets and is a key growth market for ABN AMRO in Asia.
"This transaction presents tremendous opportunities to accelerate our activities in the Pakistan market as we bring together our global expertise and resources with Prime Bank's local client base and extensive distribution network," he added.
The deal will make Amro one of the top-ten banks in the country, with assets of $2,029 million.