"It is an honour and pleasure to come back this year and I am very proud to chair the jury. The cinema flows through the veins of the planet and this festival is the heart."
The 72nd edition of the festival will run between 14 and 25 May. Last year the Australian actress, Cate Blanchett, led the jury. It gave the top prize - the Palme d'Or - to the Japanese director Hirokazu Kore-eda for the film Shoplifters.
"With the jury, we will have the privilege of being the first viewers of our new colleagues from all over the world," added Inarritu. "It is a real pleasure and a great responsibility that we will take with passion and dedication."
Inarritu is one of a troika of Mexican filmmakers who have dominated the Academy Awards in recent years. On Sunday, Alfonso Cuaron won the Oscar for the best director for his film Roma.
In 2018 Guillermo del Toro claimed the trophy for The Shape of Water.
In 2015 and 2016, Inarritu hoisted the Oscar for best director for Birdman and The Revenant respectively.
"Not only is he a daring filmmaker full of surprises, Alejandro is also a man of conviction, an artist of his time," said Cannes director Thierry Fremaux.