George Papandreou, the Greek prime minister, said his talks with Erdogan will include discussion of Turkey's bid to join the European Union.
Greece supports Turkish accession, which has been delayed for years.
Turkey went through a banking crisis in 2001, so Erdogan may offer advice to his Greek counterpart, currently implementing a series of tough austerity measures to address a debt crisis.
Education will be another issue on the agenda with Turkish officials having reportedly promised to change passages in textbooks which portray Greece as a threat to Turkish sovereignty.
Turkey and Greece are both Nato member states, but they have been rivals for decades, particularly over Cyprus.
The island has been split since Turkey occupied its northern third in 1974, a response to an Athens-engineered Greek-Cypriot coup aimed at uniting the island with Greece.
The two countries also disagree on sovereignty in some areas of the Aegean.
Turkish fighter planes routinely fly in airspace claimed by Athens, leading to regular mock dogfights with Greek jets.
Though the dogfights are usually harmless, a Greek pilot died in 2006 in a mid-air collision.
Erdogan's last official visit to Athens came in 2004. He cancelled a scheduled trip last year for health reasons.