The three pilots were among a group of eight who fled to northern Greece by helicopter and sought political asylum.
They intend to appeal, their lawyers said.
Tuesday's ruling came a day after the same appeals court rejected extradition requests for three of the eight Turkish officers.
The BBC's Kostas Kallergis in Athens said the latest ruling puzzled many in court, following Monday's decision.
The remaining two officers are due to appear in court on Thursday.
At Tuesday's hearing, the court rejected extradition for the alleged offence of trying to assassinate the Turkish president, but accepted the requests for charges of trying to dissolve the republic; attempting to dissolve the constitution and for taking the helicopter.
The pilots deny involvement in the coup and say they will not receive a fair trial in Turkey.
In the wake of the coup attempt, tens of thousands of people from every level of Turkish society have been purged from their jobs, including military officers, government officials and schoolteachers.
Critics of President Recep Tayyip Erdogan say he has used the failed uprising as a way of removing his opponents and tightening his hold on power.
A Greek court has ruled that three Turkish military officers implicated in July's failed coup should be extradited to stand trial in their home country.