The administrators said 24 stores will close on 12 September, while the remaining 28 will be closed two days later.
The retailer also plans to lay off 299 employees at two distribution centres in Worksop and Newport.
Last month, Wilko filed a notice of intent at the high court to appoint administrators and later collapsed into administration.
PwC’s Zelf Hussain, Jane Steer and Edward Williams were appointed as joint administrators on 10 August.
The administrator revealed plans to close a majority of its stores within weeks as efforts to find a buyer did not materialise.
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Earlier this month, PwC announced that 269 positions at Wilko’s support centre in Worksop, Nottinghamshire, and 14 roles at its subsidiary, Kin Limited, will be made redundant.
Edward Williams said: “In the absence of viable offers for the whole business, very sadly store closures and redundancies of team members from those stores are now necessary.
“We know this has been a deeply unsettling time for everyone concerned and would like to express our gratitude to all Wilko team members for the dedication and support they have continued to give the business in the most trying of circumstances.”
In a statement B&M said that the maximum aggregate consideration of £13m ($16.35m) is entirely funded from existing cash reserves.
The deal is not conditional on any regulatory clearances.
Workers at the acquired stores would not be transferred over and would be made redundant, the BBC reported, citing trade union GMB, which represents around 4,000 Wilko staff.