Deputy First Minister Nicola Sturgeon today gave her formal approval to the TIF plan.
The Scottish Government and Glasgow City Council believe the scheme will unlock hundreds of millions of private investment in retail and leisure.
However, critics of the scheme – who point to alarming levels of shop vacancies and the retail downturn – fear helping Buchanan Galleries to expand will hurt other parts of the city centre.
The project will also bring much-disputed changes to George Square and improvements to Queen Street Station and the Royal Concert Hall.
Government and council bosses have already dubbed the neighbourhood to be created Buchanan Quarter.
Ms Sturgeon said: "Big building projects like Buchanan Quarter are not just about the improved infrastructure we gain, they are about the employment and the training that takes place during construction.
"This development will continue the regeneration of the city centre, improving the public spaces and creating modern, vibrant new facilities that will cement Glasgow's position as a major international destination for visitors.
Under the plan, the city council will borrow about £80m against future business rates they hope will be generated by the scheme.
More than half of this money will then be handed to the owner of Buchanan Galleries to improve the area around the mall.
Liz Cameron, city council spokeswoman for regeneration, said today's decision was a "huge vote of confidence for Glasgow".