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The Barnsley said in a statement that its reasoning behind the takeover was to protect itself against the possible loss of up to £10million invested into Icelandic banks.
The move is another harsh reminder of the latest trend towards further consolidation among Britain's building societies.
The takeover is due to be completed by the end of the year, an action that is going to take place without a vote of members.
The Barnsley and the Yorkshire said in a joint statement: "The proposal follows swift, pre-emptive action from the board of the Barnsley in approaching the Yorkshire to seek a merger after the identification of possible losses of deposits with Icelandic banks."
Last month, Britain's largest building society, the Nationwide, agreed to takeover the Cheshire and the Derbyshire.
The Barnsley is the latest to fall victim to the break-down of the Icelandic banking system, which has frozen access to several hundred thousand UK savers accounts held with Icesave bank, as well as other Icelandic banks.
The Yorkshire is Britain's third largest building society with 1.9 million members and 136 branches.
However, the Barnsley has just 60,000 members and 8 branches making it the 34th largest society in the Britain based on total assets of £376 million.
The Barnsley said that although it could have managed with the loss of the £10million deposits with former Icesave, it had made the choice to be taken over by a larger society as it would be in the best interests of its members.