The building, which will be adjacent to Old Trafford, is to be funded by money raised from Neville's testimonial match in May 2011.
The ten-storey building will have 139 hotel rooms, bars, restaurants, a club shop and facilities for fans to watch United matches on projector screens. The building's exterior will be decorated in the club's colours of red and black.
"I am in favour of this application, despite being an avid Blue and season ticket holder," said Councillor Mike Cordingley.
"It is an imaginative design and in a space that is currently underdeveloped. It is really clever how they have fitted the development on the proposed site and have done a great job making something out of nothing."
Steve Burne, managing director at AEW Architects, added: "We've worked with Gary Neville on several projects and are delighted to be involved in the application for the supporters' club, this is a genuine chance for Gary to give something back to the fans."
Neville is now a Sky Sports pundit following his retirement from the game.