Developer Allied London bought the Quay Street site in a joint venture with Manchester City Council and plan to build flats, shops and offices there.
The ITV soap was filmed there from 1982 until January 2014, when production moved to MediaCityUK at Salford Quays.
Manchester City Council's planning committee voted to approve the redevelopment at a meeting on Thursday.
The move comes despite more than 2,000 people signing an online petition in the hope of preventing the set from being knocked down.
Campaigners had particularly called on developers to retain the Victorian terrace featuring the Rovers Return Inn and the soap's corner shop in their regeneration of the 13-acre site.
English Heritage rejected the application for listed status for the old Granada Studios site made by an anonymous individual in 2012 because it was not considered sufficiently historic.
The development will form part of the wider St Johns area, which is also set to feature a new Â£110m theatre and arts venue called The Factory.
The former Coronation Street set in Manchester is to be demolished, despite a campaign to save it.