Zahra Nemati, Saeed Hasani poor and Arash Smaeeli were other candidates running for this position and Mojtaba Abedini and Afshin Norouzi registered for the co-chairman's position.
Saei received eight out of 15 votes to secure the position.
Archer Zahra Nemati - a two-time Paralympic champion - finished second in the voting.
Fencer Mojtaba Abedini was elected vice-chairman, edging out table tennis Afshin Norouzi.
Judoka Arash Smaeili, twice a world champion, previously chaired the Athletes' Commission.