The Turkish NTV broadcaster reported earlier in the day that a Turkish court had ruled to release the border guards from custody, but the servicemen were still not allowed to leave Turkey, as the hearings on their case were to continue.
"We expect them tomorrow," the source said.
According to a statement by the press service of the Greek prime minister, a plane with the soldiers on board is expected to land in Thessaloniki after midnight on Wednesday.
"Under the order from Prime Minister Alexis Tsipras, a plane with Georgios Katrougalos, the [Greek] deputy foreign minister, and Deputy Chief of Hellenic National Defense General Staff Konstantinos Floros will depart on [Tuesday] night… to take the two Greek soldiers. It is expected that the plane will land in Thessaloniki after midnight," the statement read.
Relations between Ankara and Athens are tense due to a standoff over a group of eight Turkish soldiers who fled to Greece after the 2016 failed coup in Ankara.
Turkey demands that Greece extradite the servicemen, but Athens refuses to do so citing concerns that the officers will not face a fair trial back home.