The Russian state had been chasing damages from the bank after one of the company's vice presidents, Lucy Edwards, helped to transfer $7 billion out of Russia between 1996 and 1999.
Ms Edwards pleaded guilty to two charges relating to the money in a US court following a Department of Justice investigation, but Bank of New York Mellon officials maintained the bank was not involved in or aware of the transfers.
However, Russia's Federal Customs Service instigated legal action against the bank in 2007 in a bid to win $22.5 million in damages.
The case has now been dropped after the Federal Customs Service acknowledged it could not hold Bank of New York Mellon responsible for Ms Edwards's actions.
As part of the agreement to conclude the case, Bank of New York Mellon will pay $14 million towards the Federal Customs Service's legal costs.
Written by Asim Shah