When the new bank comes into force in April next year, the partners are planning to open joint branches and integrate their computer systems to improve business arrangements.
The new entity is expected to have total assets worth ¥17.3tn ($142bn) which is more than the ¥16tn ($133bn) the current leader Fukuoka Financial Group has.
The regional banks expect the new entity to boost group net profit by 17%.
The plan is yet to be approved by the shareholders of the banks, and both the banks are expected to hold their respective general meetings on December 21.
Bank of Yokohama president Tatsumaro Terazawa is likely to become the president of Concordia Financial Group, and Higashi-Nippon Bank President Michito Ishii will be the vice-president.
The banks said a decision to merge was taking due to the shrinking market size in regional economies prompted by aging and declining population, while the number of banks servicing them has not declined.