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.

The meeting will be attended by police officers, lawyers and Scotland's Lord Advocate James Wolffe QC.
The focus will be on how leaving the EU could affect law enforcement and criminal justice in Scotland.
It will also look at the possible implications for civil and family law, and commercial issues.
The meeting, which will also include experts from the Scottish Universities Legal Network on Europe and the Standing Council on Europe, is due to take place in Edinburgh on 24 November.
Mr Matheson said: "The UK Brexit vote raises many uncertainties for Scotland's unique justice system.
"That is why I am bringing together leaders and experts to help us understand these issues - and any steps we can take now to mitigate the risks.
"The cessation of EU membership and single market access would have significant and wide-ranging ramifications from a justice and legal perspective.
"The issues range from tackling cross-border crime through to an individual with an EU ex-partner securing child maintenance payment, from Europol co-ordination with other countries to protecting Scots consumers' rights when buying from abroad online."
It follows a court ruling that parliament must vote before the UK can start the process of leaving the EU.
The ruling means the UK government cannot trigger Article 50 of the Lisbon Treaty - beginning formal exit negotiations with the EU - on its own.
The justice secretary added: "The summit discussions will help inform us of risks like these - and others - as the Scottish government continues to press for full involvement in all negotiations between the UK government and the EU.
"Despite the uncertainties caused by the threat of Brexit, we will continue our efforts to safeguard Scotland's communities and the integrity of our justice system, while protecting the personal and commercial interests of our families, consumers and businesses."
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.
[NEXT_CONCEPT]
Justice Secretary Michael Matheson is to host a summit of experts to consider how the UK's Brexit vote could affect Scotland's justice system.