The agency beat Abbott Mead Vickers BBDO, Saatchi & Saatchi and 101 to secure the business.
Verde is the project name for the bank that will be rebranded as TSB from summer 2013. This follows the acquisition of 632 Lloyds Banking Group branches by the Co-operative Group for an initial £350 million. Lloyds could receive an additional £400 million based on performance.
As well as advertising, Joint will be responsible for creating the new brand identity.
Paul Pester, the chief executive of Verde, said: "We have an exciting journey ahead of us and we are looking forward to working with Joint on refreshing the brand."
Collins and Exon said: "We are relishing the chance to help launch one of the defining businesses and brands of 2013 and beyond. We can’t wait to get started."
The pair previously worked on Lloyds Banking Group at their previous agency Rainey Kelly Campbell Roalfe/Y&R.