The trial will run from the second half of 2019 to early 2020.
Passengers will leave their cars close to the South Terminal entrance and – without handing over keys - the driverless robot will lift the car and store it in a secure car park.
A Gatwick spokesman said: “The system will also be connected to real-time flight information so the robot simply returns the vehicle to the parking station.
“The user then receives an SMS that the vehicle is ready and waiting for their arrival.”
Guy Stephenson, Gatwick Airport chief commercial officer, said: “The valet parking robots could revolutionise parking at Gatwick and may also become common-place at airports and other businesses across the world.
“The new service will be a convenient, personalised experience that will save passengers time, while also reducing vehicle emissions.
“With the potential to significantly increase car park capacity, this new automated system could also help the airport meet the increasing demand for air travel with only limited changes to our existing infrastructure.”
Stéphane Evanno of Stanley Robotics said: “We aim to completely reinvent the parking experience and create a seamless customer journey.
“In addition, we will be maximising the efficient use of land for Gatwick and bringing them a sustainable solution, allowing us to envisage long-term collaboration.”