Tractor Sazi, who has already signed English midfielder Harry Lee Forrester and Irish striker Anthony Stokes, has signed Dejagah and Shojaei on three-year contracts.
The details of the contracts have not been released.
Shojaei and Dejagah, who represented Team Melli in the 2018 World Cup, had been linked with a move to Esteghlal football team.
Shojaei has most recently played for AEK Athens and Dejagah was a member of Nottingham Forest last season.
Tractor Sazi finished in 10th place in Iran Professional League (IPL) last season, 30 points behind champion Persepolis.