It is buying Arran Mall and the former Hourstons store on Alloway Street in order to transform the site into the new hub.
The scheme is part of the council’s ambition to regenerate Ayr High Street. Councillor Peter Henderson, leader of South Ayrshire Council, said: "This is an important step towards repositioning Ayr High Street as a prime cultural, heritage and leisure destination.
"A modern leisure facility will help attract people back into the town centre, support local businesses and ensure South Ayrshire is an even better place to live."
Consultation had found that bringing a leisure facility into the centre of Ayr would address concerns that the Citadel leisure centre is too remote and not easy to access, especially for younger people.