The announcement by the German interior ministry on Friday follows a similar agreement reached with Spain last week.
Both deals come after a dispute between Chancellor Angela Merkel’s conservatives and their Bavarian allies over returning asylum seekers that nearly split them and brought down the government.
“The signature of an administrative agreement with Greece is a further step on the way to more orderly conditions in European migration policy,” German Interior Minister Horst Seehofer said in a statement.
Ministry spokeswoman Eleonore Petermann told a news conference the Greek agreement, like the one with Spain, would allow Germany to send migrants entering via Germany’s border with Austria to Greece within 48 hours.
In exchange, Germany agreed to deal with a backlog of family reunification applications by the end of 2018, and to reconsider disputed cases, the ministry said.
Petermann said Germany was also in “very advanced” negotiations on a similar deal with the Italian government and she expected a deal to be struck. Last Friday, Petermann said both Italy and Greece had made counterdemands.
The deals are not likely to affect many refugees.
Figures from the Interior Ministry last week showed that since mid-June around 150 people who had already applied for asylum in another European Union country had been detected entering Germany from Austria.