Gabriele Gravina revealed he would step down as the country's top football official following a meeting held at the FIGC's headquarters in Rome on Thursday.
His announcement came a day after Sport Minister Andrea Abodi called on him to resign.
Four-time World Cup winners Italy fell at the play-offs again on Tuesday, this time after a penalty shoot-out against Bosnia and Herzegovina, and will miss this summer's finals in the United States, Canada and Mexico.
The shock waves of the latest humiliation for one of the world's most successful football nations forced Gravina, 72, to go back on his initial plans to wait until a FIGC board meeting next week to announce a decision on his future.
The FIGC said in a statement that a vote for a new president would be held on June 22nd.
Giovanni Malago, the former long-time head of the Italian Olympic Committee who was president of the Milan-Cortina Winter Olympics organisation committee, is reportedly one of the names in the hat.
Before then, head coach Gennaro Gattuso is expected to also step down, while general manager Gianluigi Buffon, the former Italy goalkeeper, announced his resignation on Thursday.
Italy's failure to reach the first-ever 48-team World Cup - which will feature the likes of Cape Verde and Curacao - led Abodi to release a statement saying: "It's clear that Italian football needs to be rebuilt from the ground up and that starts with changes at the top of the FIGC."
That came a day after Gravina had hit out at politicians "who have only pushed for resignations", while also admitting Italian football "is in a profound crisis".