The decision, published in the government gazette on Monday night would hand over the airports including several on popular tourist island destinations to Fraport AG, which runs Frankfurt Airport, among others across the world.
The deal, worth €1.23bn euros (£0.9bn/$1.37bn), is the first privatisation decision taken by the government of Alexis Tsipras, who was elected prime minister in January on promises to repeal the conditions of Greece's previous two bailouts.
The government initially vowed to cancel the country's privatisation programme but Tsipras caved in to win a deal on a third international bailout for Greece, worth €86bn. Without the rescue loans Greece would default on its debts and risk being forced out of the euro.
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.
The finance ministry's amendments, also published in the government gazette, include allowing Greeks to send up to €500 abroad per person per month, and allowing up to €8,000 per quarter to be sent to students studying abroad to cover accommodation costs.
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.
The government restricted banking transactions in late June to prevent a bank run after Tsipras announced a referendum on creditors' terms for a new bailout.
The bailout deal is getting its final approvals in parliaments in several European states. Lawmakers in Spain and Estonia approved it on Tuesday while those of Germany and the Netherlands are expected to do so on Wednesday.
Tsipras is widely expected to call a confidence vote in his government this week, after dozens of Syriza lawmakers voted against him during the ratification of the new bailout deal in Parliament last Friday.
Comment: This is so nauseating. In a nutshell: First, create problems, and then create solutions, profiting handsomely all the while. When you're done, the target country will be entirely owned by foreign corporations, and the people will be up to their ears in debt which they'll never be able to pay off. Economic slavery for the people of Greece.