Sir Alex, manager of Aberdeen FC when they won the European Cup Winners’ Cup in 1983, said the £140m City Garden Project would "reinvigorate" the city.
The site, Union Terrace Gardens, is a sunken garden with grass, paths and beds. On a recent visit, Sir Alex said the city looked "somewhat down at heel and in need of a kick-start".
Last month competition judges chose a design with bridges, ramped areas of grass, trees and a gallery to replace what’s there now.
Landscape architect Olin Studio is working with internationally acclaimed practice Diller Scofidio & Renfro and local company Keppie Design
"The winning design celebrates and reinterprets the topography of the city and the dramatic cascade of the Denburn Valley," said the judges.
Aberdeen businessman Sir Ian Wood has pledged £50m towards the project and a public referendum is being held next month to decide if the project should progress to planning.
Meanwhile a report by PricewaterhouseCoopers suggests the planned transformation would create 6,500 jobs and generate more than £120m for Aberdeen’s economy every year.
A failure to support the project would be seen as a "sign of Aberdeen’s unwillingness to support any significant public investment in the city centre", said project director Gerry Brough.
But campaign group Friends of Union Terrace Gardens criticised a call for £300,000 from the local authority to pay for drafting and negotiating legal agreements.
Chairman Mike Shepherd said: "At a time when our amenities and services are being drastically cut this is a shocking abuse of council funds. It is time to call a halt to this wasteful project."