The freehold of St Annes Mansions, Montefiore Road, Hove, has been bought at auction for £550,000.
The property comprises seven flats, with ground floor units used as shops and catering premises.
There are also 12 garages on-site.
The current annual rent for the entire building is £44,544.
Auctioneer John Hole, of Parsons Son and Basley, said: "Our day-to-day knowledge of the auction market helped our client to take full advantage of this unusual opportunity to buy a well-known building as an investment.
"There is a strong income stream from the shops. One of the services we offer is to trawl through the variety of property for sale and keep our clients advised of what is available."
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