Recep Tayyip Erdogan said the Turkish flag and that of the Free Syrian Army (FSA) had been raised in the northwestern Syrian town, which was previously controlled by the Kurdish militia known as the People’s Defence Units, or YPG.
In the centre of Afrin, “symbols of trust and stability are waving instead of rags of terrorists”, he added.
The president said “most of the terrorists have already fled with tails between their legs”, and that his country’s “special forces and members of the Free Syrian Army are cleaning the remains and the traps they left behind”.
Kurdish news websites showed images of Syrian fighters destroying a statue symbolising Kurdish new year celebrations that are being held this week.
“Afrin city centre is under control as of 8.30 this morning,” Mr Erdogan announced at a rally marking the 103rd anniversary of the Gallipoli campaign during World War One.
In a statement, Turkey’s armed forces said troops were combing the streets for mines and improvised explosive devices.
Free Syrian Army spokesman Mohammad al-Hamadeen said they entered the town from the north, east and west.
“It’s empty of (YPG) fighters,” he said. “They cleared out.”
But a Kurdish official, Hadia Yousef, said YPG fighters had not fled, and had evacuated remaining civilians because of “massacres”.
Clashes in Afrin were still under way, she said.
The UK-based Syrian Observatory for Human Rights said fighting continued on Sunday morning.
It added that while almost 200,000 people had fled the area in recent days amid heavy airstrikes, thousands of civilians remained.
It said around half the town was controlled by Turkish and FSA fighters.
The Observatory, along with the Kurdish militia, said Turkish jets struck Afrin’s main hospital on Friday, killing over a dozen people. The Turkish military has denied the allegations.
Kurdish forces were backed by the US in their campaign to oust Islamic State militants from their former stronghold in Raqqa, Syria.
Turkey views Kurdish forces in the Afrin area as terrorists linked to the outlawed Kurdistan Workers’ Party, or PKK.
The PKK has waged an insurgency within Turkey’s borders for more than three decades.
Ankara launched its campaign eight weeks ago and says it will extend the offensive to other Kurdish regions.