The elite academy, a circle of writers and intellectuals founded in 1635, voted on Thursday to accept Assia Djebar, who has written extensively about the life of Muslim women.
"With this election, which honours her as much as our country, the Academie once again shows its attachment to diversity and dialogue of cultures," Chirac said on Friday.
Djebar, a filmmaker and author, has become one of North Africa's most widely acclaimed writers with novels such as So Vast the Prison. She writes in French and her books have been translated into many languages.
"I'm not a symbol," Djebar, 68, told Le Figaro daily newspaper.
"Each of my books is a step towards the understanding of the North African identity and an attempt to enter modernity"
"My only activity consists of writing. Each of my books is a step towards the understanding of the North African identity and an attempt to enter modernity," she said.
Djebar becomes one of 40 members permitted to flaunt the green embroidered jackets, two-pointed hats and swords of France's most prestigious club.
The Academie has accepted foreigners in the past and counted writers such as Victor Hugo and Voltaire among its members.