Council planners approved the application for the scheme in the car park of the Asda store on Cherry Tree Road, Marton, using delegated powers.
A council report setting out the decision says: "Economically, the development would support the existing retail offer at the site, serving as an ancillary service for visitors to the adjacent Asda store and other retail units."
Matt McIver, chief operating officer for Cidari Multi Academy Trust, had objected on behalf of St George's secondary school which is opposite Asda, and Baines Endowed Primary Academy on Penrose Avenue.
He warned there were already "challenges in preventing pupils using the fast food outlets available in the vicinity and which many pass on the walk home."
In documents submitted to planners, he said the development contravened the council's efforts to encourage healthy eating, while additional traffic drawn to the drive-thru could put pupils' safety at risk.
He said: "I am unsure how siting this fast food outlet aligns with the healthy schools agenda, and the initiatives within Blackpool itself to promote healthy lifestyles in the young people of the town and reduce exposing them to unhealthy foods marketing."
He added: "This is already a busy road and there are long running concerns over how pupils use the crossings and their locations. This is a sensitive issue for the school since the death of a pupil in 2004 whilst crossing Cherry Tree Road. "
Setting out its decision, the council said while work was being done "to address the proliferation of hot food takeaways", the character of the drive-thru "would be different."
The report adds "the restaurant section of the development would be likely to be used by patrons of the retail park and the drive-thru section of the development would be regulated by the legal driving age of 17. "
Council highways chiefs said the development, which will create up to 30 jobs, would have no impact on traffic flow, and ruled out any safety concerns.