Donadoni only took over as national team boss after Marcello Lippi stepped down in the wake of their 2006 World Cup triumph.
The Italian Football Federation (FIGC) made the announcement on their official website after president Giancarlo Abete met with the former Milan player.
Donadoni only signed a new contract with Italy before the start of the European Championships, but the deal was conditional on securing a semi-final berth.
They progressed to the last eight but lost a shoot-out against Spain after a negative display saw the two sides locked at 0-0 after extra time.
A statement from the FIGC read: "The Federation considers the contractual relationship with Roberto Donadoni to have run out at its natural expiry date."