The deal is the first in a wave of privatisations the government had until recently opposed but needs to make to qualify for bailout loans.
The decision, which was published in the government gazette overnight, would hand over the airports, including several on popular tourist island destinations, to Fraport, which runs Frankfurt Airport among others across the world.
The concession, worth €1.23 billion, is the first privatisation decision taken by the government of prime minister Alexis Tsipras, who was elected in January on promises to repeal the conditions of Greece’s previous two bailouts.
The government had initially vowed to cancel the country’s privatisation programme, but Mr Tsipras has been forced to renege on his pre-election promises in order to win a deal on a third international bailout for Greece, worth €86 billion.
Separately, the government slightly relaxed its restrictions on banking transactions, allowing small amounts to be sent abroad for the first time in about two months..
Greeks can now also open new bank accounts that will have no withdrawal rights, in order to repay loans, social security contributions or tax debts.