The society will be known as the Yorkshire Building Society, while the Chelsea Building Society name will be retained as a separate brand within the group.
The merger creates a society with assets of £36bn, 178 branches and 2.8 million members, second in size only to Nationwide.
Yorkshire Building Society also reported that the societies’ combined performance between 1 January and 28 February exceeded expectations, delivering a pre-tax profit and increasing lending over 200% by comparison to the same period last year.