According to the ministry of development, the circuit will be built in Xalandritsa, near Patras, Greece's third largest urban area in the hope the country can host a Formula 1 event in the future.
The total cost of the track will be 94.6 million euros, according to Bloomberg, with private company Racetrack Patras SA to oversee the project.
Greece's economy remains in deep recession, with figures showing it contracted by 6.2 per cent in the second quarter of 2012.
In August the coalition government agreed fresh spending cuts totalling more than 11billion euros in order to qualify for the next instalment of its 130billion loan from international creditors.
Greece, which hosts a round of the World Rally Championship, has never had a Formula 1 driver.