Although the process is still at an early stage, the announcement has caused great joy in his home country, the French newspaper "La Croix" reported on Thursday.
"It is a great joy for us to see the start of the beatification process.
The news has caused great enthusiasm here," said Fr Anicet Gnanvi, Communications Director of the Bishops' Conference of Benin.
"Cardinal Gantin was an extraordinary personality who left his mark both in Benin and around the world."
High offices in the Roman Curia
Born in a small village in Benin in 1922, Gantin made a career in Rome and held several important posts in the Roman Curia: he was initially active in the Congregation for Missions, then became President of the Pontifical Councils "Iustitia et Pax" and "Cor unum", before finally becoming Prefect of the Congregation for Bishops in 1984.
This was the first time that an African was responsible for the appointment of bishops in Europe, North America and parts of South America. He was also the first black curia cardinal.
However, Gantin became famous as Prefect of the Congregation for Bishops through his signature on the decree that excommunicated the traditionalist Archbishop Marcel Lefebvre.
This was triggered by four unauthorised episcopal consecrations, with which Lefebvre also realised a schism.
From 1993 to 2002, Gantin was Dean of the College of Cardinals.
After his resignation, he returned to Benin, where he lived in seclusion until his death in 2008.