The enlarged mutual will be known as the Yorkshire Building Society, although the Chelsea Building Society will be retained as a separate brand within the organisation.
The combined Society will have assets of assets of £35bn, plus a network of 178 branches.
‘This merger creates a second major force in the building society sector. Joining with Chelsea offers a great opportunity to build on the strengths of both societies and form a strong, independent mutual organisation,' said Iain Cornish, chief executive at Yorkshire Building Society.
The merger is subject to Yorkshire and Chelsea member votes in January, although the deal is expected to be approved by the Financial Services Authority (FSA) on 1 April 2010.