The South African coach takes the reins at the Iranian club supported by his technical team of Maahier Davids, Kabelo Rangoaga, Musi Matlaba and Kyle Solomon.
Mosimane has been without a coaching job since he left Saudi Arabian side Abha in June 2024.
The 60-year-old coach replaced Javad Nekounam, who parted ways with Esteghlal last month.
Esteghlal is 11th in the 16-team table with eight points out of seven matches and it is also chasing continental glory in the AFC Champions League Elite after the team finished as runner-up last season.