Luton Borough Council, whose company Luton Rising owns the airport, approved the growth plans in December.
The separate private company that runs the airport, London Luton Airport Operations Limited (LLAOL), applied to increase passenger capacity from 18 million to 19 million a year and to change the noise contours.
The government said an inquiry should review key aspects of development.
Three inspectors are expected to attend the inquiry, Richard Clegg, Sheila Holden and Geoff Underwood, the Local Democracy Reporting Service said.
A pre-investigation meeting was held by the inspectors in the council chamber at Luton Town Hall in July to outline the management of the process.
The agenda included seven areas which they considered to be the most important aspects of the application, which were air quality, climate change, noise impact, sustainability, socio-economic impact, the influence of other considerations on the overall planning balance and whether it would be consistent with the local development plan and other policies.
Environmentalists were concerned about the council’s role in granting planning permission.
Local protest group Luton and District Association for the Control of Aircraft Noise (LADACAN) said it was pleased there would be an inquiry.
Earlier this year, Andrew Lambourne from LADACAN said: “We are really grateful for the support of local MPs, councils and other groups in helping to get this resolution convened.
“We expect the hearings to shine an uncomfortable light on how the city council and airport failed to strike the necessary balance between growth and mitigation, seemingly focusing on maximizing revenue instead.”
A spokesman for LLAOL previously said it respected the government’s request for the application to undergo further investigation.
“Our project enables us to put the airport on the best possible footing for a long-term recovery that supports the local economy and creates jobs, following the worst crisis our industry has ever faced,” he said.
“This plan is consistent with our commitment to achieve carbon neutrality for our own operations by 2026 and to achieve net zero emissions by 2040.”