Hatami, 33, plays in attacking line and Nouri, 32, is a central midfielder.
Al-Zawraa is going to strengthen for the 2019 AFC Champions League, where the Iraqi football team has been drawn in Group A.
Hatami has already played in Esteghlal, Persepolis, Tractor Sazi and Sepahan and Nouri was a member of Foolad, Saba, Esteghlal Khuzestan and Paykan.
The Iranian duo will travel to Iraq in the next few days to finalize their contracts.