The new law is essential for the implementation of an EU-Turkey deal aimed at easing the uncontrolled mass movement of people into Europe.
On April 4, Turkey is due to receive its first refugees returned from Greece.
However, there are warnings of a lack of preparation on both sides, while aid agencies are concerned refugees may be mistreated in Turkey.
Greece had to amend its laws for the deal to be possible and the bill was passed by 169 members of the 300-seat parliament.
In 2015, more than one million migrants and refugees arrived in the EU by boat from Turkey to Greece, and Athens has struggled to cope.
Tens of thousands have been stranded in Greece after northern counties closed their borders.
Under the EU-Turkey deal, refugees arriving illegally in Greece are expected to be sent back to Turkey from April 4 if they do not apply for asylum or if their claim is rejected.
In return, Turkey will receive aid and political concessions.
The UN has called on Turkey and Greece to ensure safeguards are in place before returns begin, warning of “serious gaps” on both sides.
According to an Amnesty International report, Turkey has been illegally forcing thousands of refugees back to Syria.
Turkey is yet to respond to the Amnesty report but has denied sending back any refugees against their will.
Turkey has taken in 2.7 million Syrian refugees since the civil war began five years ago. Many live in camps near the border between Turkey and Syria.
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