The Queen Street restaurant and four-bedroomed accommodation has a guide price of £385,000.
One of Yorkshire's first Italian restaurants - it was established almost 50 years ago - it is on the market with Colin Ellis Property Services.
Chef patron Giorgio Alessio has decided to retire, and is being offered as a fully equipped going concern on either freehold or leasehold basis.
In May 2018 Mr Alessio posted on the restaurant's Twitter account that the owners were open to offers for the business: "Restaurant for sale. Two careful owners. One of the oldest Italian restaurants in Yorkshire since 1973. Value: Hopefully a lot of money. For rent or for sale. Only genuine enquiries please."
That attracted widespread attention; and now the sale has been made formal.
Mr Alessio has owned The Lanterna since since 1997, and has worked hard ever since to live up to the accolade given it by the influential Italian daily newspaper La Stampa, as the English temple of Italian cuisine.
The Daily Telegraph put it in the Top 8 most influential Italian Restaurants in Britain.
It has long been popular with residents and visitors, and has been lauded by food critics.
Critic Jay Rayner visited in 2011 and said it was a place to enjoy a "life-affirming meal". Daily Mail food writer Tom Parker Bowles said: "Here at Lanterna, you'll find a great cook in thrall to great ingredients. Not masking their beauty, or mucking about. It's the soul of real Italian cookery."
The estate agent's details show that the Grade II listed building has two main dining areas with 33 covers, and the kitchen includes a preparation room and wash-up area. In the basement there is a wine cellar.
The upper floors are currently arranged as an office and self-contained one bedroom flat at first floor level with a further three-bedroom self-contained maisonette above.
It is for sale freehold as a going concern including business goodwill and fixtures and fittings. The owners may consider selling the business on a leasehold basis at £85,000 including the fixtures and fittings with a commencing rent of £18,000 per annum for the whole building.
Colin Ellis Property Services can be contacted on 01723 363565.