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 Doha-based operation is owned by the Qatar government. Its main Arabic network is the leading pan-Arab TV news station.
Al-Jazeera Arabic can be outspoken on subjects deemed as sensitive in the region, but avoids criticism of Qatar and its Gulf allies, specifically Saudi Arabia. It has faced curbs in several Arab countries where it has ruffled feathers.
Al-Jazeera English launched in 2006. Other offshoots include Al-Jazeera Balkans, based in Bosnia, and US-based Al-Jazeera America.
Al-Jazeera Network has more than 70 bureaux worldwide and employs around 3,000 staff.
Domestic audiences are catered for by state-run TV and radio. The large expatriate population has access to media from their various home countries.
Qatar has daily newspapers in Arabic and English. The main titles have links to the ruling family and there is little or no critical reporting of domestic or foreign policy affairs.
BBC World Service radio in Arabic, Radio France Internationale, France's Arabic-language radio service Monte Carlo Doualiya, UAE-based MBC and Radio Sawa from the US are available on FM in Doha.
Qatar has advanced internet infrastructure and is widely connected to the web. There were 2.2 million internet users by 2014 (Internetlivestats.com).
Authorities filter political criticism, material deemed offensive to Islam, pornographic content and online privacy resources.
The top social networks used in Qatar are Facebook, Twitter and Instagram.
The former Coronation Street set in Manchester is to be demolished, despite a campaign to save it.
[NEXT_CONCEPT]
Influential pan-Arab and international TV broadcaster Al-Jazeera has raised Qatar's media profile.