The sustainable fuel is blended with traditional jet fuel, with a 70% lower carbon footprint.
It will be delivered by existing pipelines from a refinery in Stanlow, Cheshire.
Operations director Rad Taylor said: "It's really game-changing for the industry."
He said: "It's essentially about using non-recyclable waste, which would typically go into landfill, and using that to generate aviation fuel so it's a real sustainable alternative."
The airport, part of Manchester Airports Group, will work with Fulcrum BioEnergy Limited UK, which is developing a new refinery for sustainable aviation fuel.
Business Secretary Kwasi Kwarteng said: "This partnership is a huge leap forward for the long-term competitiveness of Britain's aerospace sector, demonstrating how, by going green, industry can create jobs and help level-up across the UK.
"Cleaner aerospace and aviation is at the centre of our plans to end the UK's contribution to climate change by 2050."