The Former Partizan Belgrade coach penned a one-year contract with the Tehran-based team but Steel Azin didn't disclose any financial details.
Tumbakovic will join Steel Azin in an Austria training camp this week. He will be assisted by Iranian duo Afshin Peyrovani and Ahmad-Reza Abedzadeh in Steel Azin.
Tumbakovic is the most successful coach in the history of Partizan Belgrade where he won six national championships and three national cups.
From January 2004 to December 2009, he was the manager of Shandong Luneng in the Chinese Super League.