Following discussions starting in December, the deal was confirmed today, with completion expected to take place early next year.
Under the deal's terms Coventry will pay £780m for the bank, with up to £125m deferred for up to three years subject to the performance of Co-op Bank during that period.
The joint statement issued by both parties said that the Co-operative Bank board had discussed whether or not a member vote on the deal was required and 'conclusively determined' it was not following focus groups and member surveys.
Chairman of Coventry Building Society, David Thorburn, said:
"I believe this is a transformationla moment for members and customers of the Society and The Co-operative Bank. We're building on our shared heritage and creating a stronger mutual business that will deliver in the best interests of our current and future members."
Chief executive office of Coventry Building Society, Steve Hughes, commented:
"By bringing together Coventry Building Society and The Co-operative Bank we will be able to deliver more value to more people in the coming years. I am excited about the opportunities that lie ahead, most importantly our ability to sustain the great value and outstanding service that matters most to our members."