The expanded society will be called Coventry Building Society and will be based in Coventry. Total membership will increase from over 1.2 million to around 1.5 million, and the overall asset size will increase from £18.4 billion to £21.1 billion.
Coventry Building Society is one of the strongest building societies in the UK. Since the onset of the credit crunch, it has continued to report substantial profits and its strong funding and capital position has enabled it to grow throughout the economic downturn.
Coventry's financial strength will deliver an immediate benefit for many Stroud & Swindon members, who voted overwhelmingly in favour of the merger in June.
It is expected that approximately two thirds of a total of around 250,000 savings accounts will see interest rates improved on completion of the merger to match equivalent products offered by Coventry.
David Stewart, chief executive of Coventry Building Society, said: "Coventry's performance over the last 3 years has demonstrated the strength of our traditional building society model. I believe that the merger with Stroud & Swindon Building Society will help us build on recent successes and bring the benefits of our prudent and member-focussed approach to a wider membership."