The deal, the value of which was undisclosed, is expected to be completed in the third quarter of this year, pending approval from the relevant regulatory authorities.
Once the acquisition is formally finalized, ABN Amro Mellon will be integrated into the newly formed Bank of New York Mellon Corporation.
Nadine Chakar chief executive of ABN Amro Mellon said: "Following its decision to merge with the Bank of New York, Mellon was keen to explore the possibility of taking full ownership of ABN Amro Mellon.
"Both shareholders are in agreement that such a change of ownership is in the best interests of the JV and its clients. ABN Amro remains one of our most important clients we will continue to be ABN Amro's preferred provider."
The merger between Mellon and Bank of New York, which was initially announced in December 2006, was concluded this week.
The new company manages asset of some $1 trillion and services debt of over $11 trillion.