Two Turks were to be handed over to the Egyptian embassy and deported after questioning, while three Egyptians were to be released on a 10,000 Egyptian pound ($630) bail, the prosecutor said in a statement.
On Wednesday, Turkey had summoned Egypt's charge d'affaires to deliver a protest about the raid and detentions.
Egypt in turn summoned Turkey's charge d'affaires, Egyptian media reported on Thursday.
Ankara's relations with Cairo have been frosty since the Egyptian army ousted Muslim Brotherhood president Mohammed Mursi, an ally of Turkish President Tayyip Erdogan, in 2013. The two countries have also been at odds over maritime jurisdiction and offshore resources in the eastern Mediterranean.
Anadolu said just one Turkish national had been detained and later released after the raid.
"Hilmi Balci, one of our four employees detained in Egypt, has been released. We expect the others to be released on bail," Anadolu quoted its general manager Senol Kazanci as saying.
The Egyptian interior ministry said the location of the raid - which it said was a flat - had been used to produce false and "negative" information.
It accused Turkey and the banned Muslim Brotherhood of being behind "adverse activity" at the flat. Egypt's State Information Service, which accredits foreign media, said Anadolu had no legal status in the country since 2013.Turkey's Foreign Ministry condemned the raid as "an act of violence" against Anadolu.