The Derbyshire and the Cheshire societies will be allowed to keep their branding under the terms of the deal, in which no money will change hands.
Their shareholders will therefore not receive any windfall bonuses from the three-way merger.
For its part, Nationwide sought to dampen speculation that they had been asked to step in and take over the firms by the regulator, due to their financial troubles.
The lender's chief executive, Graham Beale, said: "The Financial Services Authority has been aware of the dialogue and we needed their support in terms of approving the structure of the transaction, but really that has been the extent of their involvement."
He added: "The Derbyshire and the Cheshire have independently concluded that a merger with Nationwide is in the best interests of their savers and borrowers given the financial issues faced by both societies."