It is hoped that the development will rival top water parks in Dubai and Florida and attract up to half-a-million visitors a year.
Coun Fox said the decision should also kickstart The Sands project – a wider regeneration scheme for the North Bay.
Using powers delegated to him by the council, Coun Fox has approved the proposals from Benchmark Properties, following an detailed assessment of the developer’s plans.
The council is now set to provide a loan for up to £9m of the £18m cost of the water park.
The attraction, which it is said will be the only one of its kind in the UK, will be built on Burniston Road car park and could be open by Easter 2016. It will be run by German company Alpamare.
The council said that initially it will feature “four thrilling water rides, which will be some of the best rides available in the world on a par with those found at premier water parks in Dubai and Florida”. There will also be a wave pool, a luxury spa suite and an outdoor infinity pool.
Coun Fox said: “The decision is a significant milestone and should be the catalyst that will get The Sands project moving once again and bring massive economic benefits.
“While there is an element of risk, it shows the confidence we have in the scheme and demonstrates the council’s strong commitment to economic growth, regeneration and jobs.”
Roland Duce from Benchmark added: “Scarborough’s place in history as the first seaside resort is assured, but it’s important the town continues to evolve in order to attract new generations of visitors. The water park will be a world-class attraction of the very highest calibre.”