The plan would consolidate Yorkshire Building Society's position by creating a group with assets in excess of £35 billion ($58 billion).
The combination, with 2.7 million members and 178 branches, will focus on the traditional building society business of residential mortgages and savings and will be principally retail funded, the companies said.
The enlarged society will be known as Yorkshire Building Society, with the Chelsea Building Society name retained and operated as a distinct brand. Subject to approval from regulators and eligible members of both societies, the deal is expected to be completed by April 1, the companies said.
"The enlarged society will continue to have one of the strongest capital positions of any major United Kingdom bank or building society and a secure funding base.
Positioned to prosper
"As far as Yorkshire is concerned, we are seeing more positive signs and this merger will ensure that we are extremely well placed to prosper as markets recover," said Ian Cornish, Yorkshire's chief executive.
The Yorkshire Building Society recorded a net loss of £15 million in the first half of the year, while Chelsea Building Society had a net loss of £19 million.
Unlike banks, building societies are owned by their members.
They offer a range of banking and other financial services, but generally specialise in mortgage lending.
The Yorkshire had two million members and assets of more than £20 billion as of June 30. Chelsea, with 700,000 members and assets of £14 billion, is the country's fifth-largest building society.
A year ago, the Yorkshire took over Barnsley Building Society to help it withstand millions of pounds of losses from the collapse of Iceland's banks.
- AP