He joins from Bank of Maldives where he has been CEO and managing director since 2014.
His appointment follows the decision by Kevin Wilson to stand down after 14 years as chief executive, who will remain in post until December.
Andrew Healy brings more than 25 years of experience in financial services to his new role, including over 10 years at CEO and board level. He started his career with Natwest and has worked in senior roles in both Europe and Asia.
He is a current board director of the Asian Banking Association and a former chairman of the Northern Ireland Banking Association.
The society’s chair, Rachel Court, said that the board was unanimous in its choice of the new CEO.
Andrew Healy said that he is delighted to be given the opportunity to continue Kevin Wilson’s work at Leek United.
He added: “In an increasingly crowded and challenging financial services landscape, I look forward to helping to positively differentiate the society in a way that fully recognises its fine traditions, loyal members and hardworking staff.”