A European diplomat, who wished to remain anonymous, said: "The fact that he is finally going is very significant and should not be underestimated.
"Although we expect no big announcements, it is a historic visit that can only do good."
Relations have gradually thawed since the two Nato allies nearly clashed in 1996 over a deserted Aegean island, with war only averted through US intervention.
A senior Greek government official who requested anonymity said: "We want to go ahead with the complete normalisation of relations and we expect the other side to respond."
Greece, eager to bring its neighbour closer to Europe, backs Turkey's EU accession, provided it completes reforms and works to re-unite Cyprus, which is already an EU member.
Turkish Cypriots voted for reunification in 2004, but Greek Cypriots opposed it.
Addressing the Greek parliament on Friday, Karamanlis said the government had "neither excessive optimism nor pessimism" over the visit.
"We are seeking the gradual restoration of mutual trust. We are working for the full normalisation of Greek-Turkish relations, which, of course, also presupposes a resolution of the Cyprus issue," Karamanlis said.
|Turkish and Greek fighter planes are often|
involved in dogfights over the Aegean [AP]
His uncle, Constantine Karamanlis, was the last Greek prime minister to visit Turkey officially in 1959, though unofficial visits have taken place since.
In November, Karamanlis inaugurated a pipeline with Recep Tayyip Erdogan, Turkey's prime minister, on the Greek-Turkish border.
During the January 23 to 25 visit, he will visit both Ankara and Istanbul, where he and Erdogan are expected to attend a business forum on transport links, including possible direct flights between Athens and Ankara.
Semih Idiz, a commentator for the liberal Turksih daily Milliyet, said: "Greek economic interests in Turkey are growing fast, despite the occasional reports of dogfights over the Aegean."
Greek banks, who have long invested in the Balkans, have recently turned to Turkey, with National Bank, a leading Greek financial company, buying Turkish Finansbank in 2006.
Apart from Cyprus, major sources of tension remain minority rights in both countries and disputes over areas in the Aegean.
The two sides are expected to urge the United Nations to re-engage in efforts to re-unite Cyprus, divided since Turkey invaded in 1974 in response to a Greek-inspired coup in Nicosia.