"Units of the Free Syrian Army, which are backed by Turkish armed forces, took control of the centre of Afrin this morning at 8:30 am (0530 GMT)," Erdogan said, adding that de-mining operations were under way.
Taking Afrin has been the main objective of Turkey's operation Olive Branch, a deadly ground and air offensive launched on January 20 with the aim of ousting the People's Protection Units (YPG), a Kurdish militia group.
News of Afrin's capture was also confirmed by the Turkish military, which released a statement saying the city centre was "under control".
"Search operations to locate mines and other explosives are under way," it said.
"Now the Turkish flag will fly over there! The flag of the Free Syrian Army will fly over there!" said Erdogan who was speaking at a ceremony marking the battle to open the Dardanelles during World War I.
As the Turkish operation intensified, more than 200,000 civilians fled the Kurdish-majority city in less than three days, according to the Britain-based Syrian Observatory for Human Rights.
Ankara sees the YPG as a Syrian offshoot of the outlawed Kurdistan Workers' Party (PKK), which has been waging an insurgency inside Turkey since 1984.
But Washington has provided weapons to the YPG, which it sees as a key ally in the fight against jihadists in Syria and Turkey, with Ankara's military operation hiking tensions between the two NATO allies.
According to figures released by the Turkish army, 46 Turkish soldiers have been killed since the start of the Afrin offensive.
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