The building, on South Cliff, is Grade II-listed and home to popular Mexican restaurant El Gringos, whose future is now uncertain.
Ink Lounge Bar, which occupied the basement of the Villa Esplanade, announced in April that it would not be reopening after the coronavirus pandemic as the owners decided to retire.
Tom Cunningham, hotels director at Savills, said: "Villa Esplanade presents an exciting opportunity for redevelopment in an excellent seafront location.
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"The characterful property, with its original quirks and features, has created unique development potential and we’re pleased to have completed on the sale."
Wright Investments gained approval to turn the former hotel into 26 self-contained apartments in April.
A separate application in May gave the developer the green light to transform the ground floor restaurant, El Gringos, and basement nightclub Ink Bar into two more flats.
The plan was approved under delegated powers by Scarborough Council officers after the 26-flats on the upper floors were granted permission by councillors on the authority’s Planning Committee.
In a report into the extra two flats, it notes that the current occupiers of the restaurant, El Gringos, had objected.
Their objection stated: “Our business is strong and profitable, employing a number of people and whilst this last year has been difficult, we are extremely optimistic for the future and we would like to continue trading from our current premises.”
However, the report noted that officers could give no weight to the restaurant’s objection when making a decision, adding: “Whilst this concern is noted any issues relating to the tenancy are not material planning considerations and cannot be taken into account as part of this assessment.”
The former hotel, which dates back to 1834, has not operated as accommodation for more than a decade.