Garance made landfall on Friday (28 February) and was the most severe storm to hit the island since 1989, bringing 100mph winds and prompting fresh guidance from the UK Foreign Office.
However, despite the airport reopening, passengers have been strongly advised not to attend and to instead contact their airline for further information about the status of their flights.
Sir Seewoosagur Ramgoolam International Airport said: "In order to ensure a smooth resumption, access to the check-in hall of the terminal will be temporarily restricted to departing passengers with valid air tickets."
The airport has been closed since 7pm local time on Wednesday (26 February).
France’s meteorological agency said Garance made landfall on the northern coast of Reunion, with 103mph winds. It was the strongest storm to hit the territory since Tropical Cyclone Firinga in January 1989.
Forecasts of heavy rainfall, strong winds and powerful waves prompted authorities to issue a purple cyclone warning – the highest level – for the whole island. Conditions are expected to remain dangerous on Friday and will begin to improve on Saturday (1 March).
The FCDO is advising Brits in the country to "stay in a safe place and follow instructions and updates from local authorities".