The eight men fled in a helicopter to Greece after the coup attempt but say they were not involved.
Turkey has demanded they return to stand trial. The soldiers say their lives would be in danger.
The case has presented a diplomatic dilemma for Greece.
Senior prosecutors had argued against agreeing to extradition on human rights grounds. The court's decision is final and cannot be appealed against.
The eight soldiers - three majors, three captains and two sergeant majors - have been labelled traitors by the Turkish government.
The issue has created new tensions between the Nato allies, who are currently working together to help negotiate a peace deal in divided Cyprus.
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.
Greece's Supreme Court has ruled against extraditing eight Turkish soldiers whom the Turkish government accuses of being involved in last July's attempted coup.