Worth's appointment is effective Sept. 1, the company said on Friday.
Co-operative Bank said current finance chief John Baines will step down on Sept. 28 and leave on Oct. 1.
Worth's appointment comes two and a half months after the bank named Liam Coleman as deputy chief executive in the expectation that he would succeed CEO Niall Booker.
Co-operative Bank has been on the road to recovery from troublesome real estate loans that left a 1.5 billion pound hole in its capital in 2013, bringing the bank close to collapse.
(Reporting by Mamidipudi Soumithri in Bengaluru)