The premises in Primrose Street was purchased at the beginning of November, sales agent Graham & Sibbald confirmed.
The building was bought by a group of investors including two Clackmannanshire businessmen.
The cost of the sale is undisclosed however the price tag was in excess of £350,000.
The sales agents envisaged the property will be demolished to make way for a new "quasi-commercial development" providing retail uses at ground floor level and up to 62 residential flats above.
Since the sale, Alloa-based architects, Machin Associates, have lodged an application with Clackmannanshire Council to demolish the store on behalf of "Alloa Development Company Ltd".
The Alloa Development Company Ltd's directors are Stirling-based Alan Loughray, and Clackmannanshire businessmen Ross Henderson and Colin Machin, both of Alva.
Andrew Mitchell of Alloa Town Centre BID said, "Fantastic news that the Alloa Development Company has purchased the building. All three gentleman involved have a proven business track record and I look forward to seeing what their plans are for the site".
The Victorian building has lain empty since the Co-op Group closed 10 of its biggest loss-making stores and put the remaining 26, including Alloa, up for sale. The town centre premises had been trading for the Co-op since 1885 and the closure in 2007 resulted in the loss of 30 full and part-time jobs.
Property developer Ken Cairnduff, director of Glasgow-based Cairnduff Developments Limited, bought the former department store building for £1.6 million in November 2006.
In early 2008 the building changed hands once again when it was sold to Glasgow-based firm, Zoom Developments Ltd, specialists in residential schemes.
A demolition warrant was granted for the building with plans mooted for large purpose built retail units aimed at attracting high street names to the town centre in its place.
However Zoom Developments Ltd went into liquidation near the end of 2010 and the building was put on the