The city council said developing the Bannerdale site, off Carter Knowle Road, posed no risk to health.
It said it had carried out extensive investigations into any potential risks.
Campaigners have raised concerns over possible health risks and increased traffic if the build goes ahead.
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The development, which includes sports facilities and a 1,200 place secondary school, attracted more than 80 objections.
However, Joel Hardwick, Schools Organisation Manager at Sheffield City Council, said: "It's really important to stress that we would never build a school on land that was unsafe.
"We know that it is a suitable and safe place to build an excellent new school to serve the south west of Sheffield."
The authority said the birth rate in Sheffield had increased by 25% since 2002, with 1,000 more children per year entering education.
It said the area earmarked for the school was a popular location for young families and the additional places were needed to meet demand.
Opponents said air pollution and traffic congestion were already a problem in the area and would be made worse by the school, which they claimed was not needed.
They also raised concerns about possible health risks posed by waste from the former landfill site, and the loss of green space.
The plans were approved at a meeting on Tuesday.
Plans to build a Â£25m school on a former landfill site in Sheffield have been approved, despite concerns over the suitability of the area.