The Co-operative Group has agreed terms with Lloyds Banking Group to buy 632 Lloyds TSB and Cheltenham and Gloucester branches including the branch in Teme Street Tenbury Wells.
The sale was demanded by European regulators after Lloyds bought HBOS during the financial crisis.
It is thought that existing customers will be given the choice of transferring their Lloyds account to another branch or convert to a Co-operative account.
Co-op were voted as the best current account provider 2011 by money supermarket.