The 48-year-old coach replaced Spanish coach Lucas Alcaraz, who had been appointed as head coach of Ghaemshahr-based club in December.
Elhami led Mes Rafsanjan in the first half season of the 2023-24 Iran Professional League (IPL) but the two parties parted ways last month.
This is Elhami’s third stint in Nassaji as he had coached the team in 2017 and 2022.