Workers finished the demolition of London Road Primary, in Parkhead, as Celtic bosses said the move represents a "new era" for the club.
In its place, the club plans to build an official superstore, museum, theatre, cafe, ticket sales, offices and associated facilities.
The plans also include a new "Avenue of Heroes" stretching from London Road to the front door of the club's stadium with sculptures of famous club figures.
A statement on Celtic's website reads: "For many, the "old school" has become synonymous with Celtic Park, and we're sure many fans will look back nostalgically on the building. However, as we look forward to embracing a new era at Celtic Football Club, we're confident that our existing fans, and our fans of the future, will reap the benefits of a new-look approach to Paradise.
"It also represents another important step in the Celtic 2014 project, which will see the club embrace a number of high-profile events scheduled to take place throughout Glasgow and Scotland during this year."
Last May, the club was given permission for the move by Glasgow City Council's planning applications committee. Although there were objections from locals who wanted to see the B-listed building preserved, football chiefs pushed ahead with plans.
Due to the age of the building and its listed status, Historic Scotland was also given a say on the plans.
It was initially planned that the works would be completed in time for the 2014 Commonwealth Games.
But it is now thought only the demolition and associated public realm works linking the stadium with adjacent Games venues will be finished on time.
London Road Primary was sold to Celtic Park by Glasgow City Council for £300,000.
Part of the old school wall will be retained as a 'historic link' and anything of architectural worth recycled in other developments.