He replaces John Goodfellow, former chief executive of Skipton Building Society, who has held the post for the past year.
Commenting on his election as Chairman, Graham Beale said: "Building societies have a history of providing long-term good value to their members, and it is important they are able to continue doing so.
“The sector faces some challenges. These include the need for a level playing field with the banks for access to funding. It is also important to ensure mutuals do not face unfair competition from nationalised, or part-nationalised, banks. The BSA also continues to be concerned at the levies imposed on societies by the Financial Services Compensation Scheme.
"Nonetheless, building societies form an important part of the UK's financial services marketplace, and I am looking forward to my time as chairman of the BSA as the mutual sector continues to build on this position."
Richard Hornbrook, chief executive of Chelsea Building Society, has taken over as BSA Deputy Chairman from Graham Beale.
