Yorkshire, which claims to be the UK's second largest building society, expects to complete the deal in the fourth quarter of this year.
At the same time as taking on the Egg brand, mortgage and savings customers, Yorkshire is in the process of a merger with smaller society Norwich & Peterborough, which is expected to complete on 1 November.
When the Egg deal completes Egg savers and borrowers will become members of Yorkshire Building Society. The savings book is worth £2.5bn and the mortgage book £430m.
Egg's credit card book was sold in April by Citigroup to Barclaycard, with Egg credit card customers becoming Barclaycard customers.
Citigroup has owned the brand for four years after buying it from Prudential for £575m in January 2007, but has been attempting to sell it for some time.
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