Under the terms of the deal, Mellon is paying a premium of around $1.8 billion for the Bank of New York, which had a market capitalization of around $26.7 billion at the close of trade on Friday.
Entitled the Bank of New York Mellon Corporation, Bank of New York shareholders will be given 0.9434 shares in the new company for each share they currently own.
The new institution will have a market value of around $43 billion, making it a top ten global asset management firm and the biggest asset custodian and corporate trustee in the world.
Mellon Financial boss Bob Kelly will become chief executive of the new company and will assume the role of chairman of the board after 18 months.
Bank of New York chairman and chief executive Thomas Renyi, will serve as executive chairman of Bank of New York Mellon directly following the merger, while Bank of New York president, Gerald Hassell, will become president of the new group.
Both Bank of New York and Mellon shares rose in trading following the announcement and the companies have predicted that the deal, scheduled for completion in the third quarter of next year, will reduce total costs by as much as $700 million a year.