Spence, who joined The Cambridge as non-executive director in 2006, has over 30 years’ banking experience, having held senior positions in investment banks.
He chairs the nominations committee, is a member of the IT transition and remuneration committees, while he is also senior bursar of Queens’ College.
Spence said: “I intend to work hard alongside my fellow directors and our staff to improve, strengthen and grow our society.”
In March The Cambridge was named Employer of the Year at the Cambridge News Excellence Awards, while it also received a One Star Award from the national Best Companies scheme.
Spence added: “These achievements help us to continue to attract the best staff to work at The Cambridge, which is key to our being able to deliver an excellent service for our customers.”
O’Reilly said: “I am confident that The Cambridge will continue to deliver the changes needed to make it the most recommended financial brand in the East of England.”
Fellow of the Chartered Institute of Management Accountants Stuart Cruickshank has also been appointed as vice-chairman.
In 2013 The Cambridge lent more than £200m to people wanting to buy or improve their homes, growing its mortgage book by 8.3%.