The £11.2m building job will transform Portslade Aldridge Community Academy over the course of the 82-week contract.
Apollo will carry out refurbishment and remodelling work, including the construction of new science, learning resource centre and sixth form building.
Apollo will also fit photovoltaic solar panels, expected to provide savings for the Academy of around £18k a year.
Managing director of Apollo Education, Jeremy Eavis, said: “We are delighted to have been awarded this significant project – the first time that Apollo Education will have worked with Brighton and Hove Council and the Aldridge Foundation.
“We are very much looking forward to drawing together all aspects of our knowledge and expertise to deliver this project, from refurbishment to new build, and incorporating elements of our EcoFit retrofitting workstream.
“The Portslade students will continue to use their school buildings, while work is in progress, and this also gives us the opportunity to showcase our experience and expertise at working in occupied schools.”