The appointment came after Chris Pilling announced he was stepping down from the position at the end of the year.
Regnier is currently chief customer officer and executive director at the Society and will take up the role of CEO on January 1 2017.
John Heaps, chairman of Yorkshire Building Society, said: “I am delighted to announce Mike as our new chief executive. His commitment to mutual values, his engaging style of leadership and his clear strategic outlook will all help to ensure he builds on the Society’s continued success.”
Heaps thanked Pilling for his contribution to the Society and wished him well for the future.
Regnier brings to the role experience in consulting and retail financial services and was responsible for the re-launch of the TSB brand on the UK high street.
He added: “I’m very much looking forward to working with the Board, the senior management team and all of our colleagues as we continue to build on our success.”