The 43-year-old Marfavi was selected by the club's chief executive, Amir Vaez-Ashtyani, on Wednesday.
Celebrated German coach Erich Rutemoller, 64, was appointed as the club's technical assistant for the next season on the same day.
The former FC Koln and Hansa Rostock coach signed a one-year deal with the Tehran-based club.
Former Esteqlal manager Amir Qalenoi resigned from his post after his squad was knocked out of AFC Champions League following a draw with Al-Ittihad.
Qalenoi resigned from his post after the match due to differences with Amir Vaez-Ashtyani. His resignation comes a week after he won Iran's Premier League title with the Blues.
The last time that the Blues had lifted a trophy dates back to the 2005-06 season when Esteqlal was named IPL champion, again, under Amir Qalenoi.