The landmark late 19th century building on Mansfield Road was one of the oldest auction houses in the Midlands but has been empty for several years after Neales effectively closed in 2009.
Before it was sold, the property was advertised by estate agents with a guide price of £1.25m.
The building will now become a church serving the city.
Neales were acquired in 2004 by the Fine Art Auction Group, parent company of Dreweatts auctioneers, which itself was bought by Noble Investments at the end of 2012. Noble in turn were acquired by the Stanley Gibbons Group less than a year later.
