The town's borough council has agreed to negotiate with an unnamed bidder to purchase the site.
The theatre was mothballed by the council in January after it said it could no longer afford to subsidise it.
The developer wants to demolish the theatre and build a roller coaster, botanical gardens and cave-themed attraction on the site.
A second bid for the site, which would have seen the theatre replaced with a restaurant and housing, was rejected by the Conservative-run council.
A third option would have been for the council to demolish the theatre and clear the site itself at an estimated cost of Â£600,000.
Campaigners who wanted to retain the 1920s-built Futurist as a theatre and cinema said they were disappointed by the decision.
The council acquired the theatre in the 1980s, but decided to redevelop the site after a report said the building was "beyond the point" of refurbishment.
A "magical" cave-themed attraction could replace Scarborough's Futurist Theatre.