In a sign of the importance of the alliance, Putin's visit to Turkey is his first trip overseas since he won a historic fourth presidential mandate in March 18 polls.
Turkey and Russian Federation have recently put aside their traditional rivalries and differences on regional issues to forge closer ties.
Last week, Turkey announced it would not be following North Atlantic Treaty Organisation and European Union allies in ousting Russian diplomats in response to the poisoning in Britain of a former Russian spy.
"The Akkuyu plant will be the 56th nuclear plant constructed in the world", Erdogan said via a video teleconference held at the presidential complex in Ankara.
In December, Ankara and Moscow finalised an agreement for Turkey to purchase Russia's long-range S-400 missile defence system.
The three leaders will discuss regional events, the ongoing war in Syria, and the relations between their countries.
The talks will focus on the war in Syria.
"We are also in close cooperation with Russian Federation to end as soon as possible the terror threat and clashes in Syria", said Erdogan.
"The Akkuyu Nuclear Power Plant is a new step to further develop Turkish economy", Putin said.
Mr Putin hailed the project as a symbol of growing co-operation between Russian Federation and Turkey.
The statement on Monday came one day after the President visited Turkish soldiers at an outpost in Turkey's Hatay province bordering Syria, Xinhua news agency reported.
Erdogan declared: "We are witnessing a historic moment".
"In the name of God!"
The Akkuyu NPP will produce 35 billion kilowatts of electricity at full capacity, which will meet about 10 percent of Turkey's electricity needs.
This will be the first such object to be built in Turkey.
The two countries are also building the TurkStream pipeline, estimated to be worth more than $12 billion, to transport Russian gas to Turkey. "We will accelerate the process", the Russian President added.