The property, in The Avenue, is among 51 former Woolworths stores which are being bought nationwide by Iceland, and one of only two in Somerset, the other being in Frome.
Iceland said it planned to create 2,500 new jobs across the country – as against the 27,000 jobs which were lost when the last of 807 Woolworths stores was shut on Tuesday.
The Minehead Woolworths was in the final batch of stores which remained open until the very end.
Woolworths had traded in Minehead since 1937 and had nearly 30 staff at the premises, some of whom had worked there for more than 20 years.
The staff are understood to have been offered an opportunity to move across to Iceland as their new employer.
An Iceland spokesman said: “We are confident we can help to support the local community in these towns who have lost a major High Street retailer in Woolworths.”
Woolworths went into administration with debts of £385 million in November and administrators Deloite were unable to find a buyer to take over the chain.
Iceland, which already has 682 stores, previously offered to buy all of the Woolworths chain last summer but the bid was rejected as ‘unacceptable’.
The frozen food retail business was founded in 1970 and was taken over by a consortium led by Icelandic investment group Baugur in 2005.
The firm already has stores in Taunton, Bridgwater, and Barnstaple.