Thiam has joined the Emirati football club for an undisclosed fee.
He was under contract with the Iranian giant but had a clause in his deal allowing him to join Ajman.
Esteghlal has signed Nigerian striker Salisu Abdullahi "Alhaji" Gero as a replacement for Thiam.
Thiam scored 12 goals in 13 matches for Esteghlal last season.