Fighters waved flags and tore down the statue of a legendary Kurdish figure after claiming the city centre on Sunday.
The two-month Turkish-led operation aimed to rid the border region of a Kurdish militia that Turkey considers a terrorist group.
Activists say 280 civilians have died, although this is denied by Ankara.
Earlier, Turkish President Recep Tayyip Erdogan announced that 'units of the Free Syrian Army... took control of the centre of Afrin this morning'.
He said operations were continuing to clear mines and any remaining resistance.
'Most of the terrorists have already fled with tails between their legs,' the Turkish president said.
'In the centre of Afrin, symbols of trust and stability are waving instead of rags of terrorists.'
Pictures and video footage emerged of forces tearing down a Kurdish statue with a bulldozer.
The monument depicted the blacksmith Kawa, a legendary figure for Kurds.
A statement on a Whatsapp group for the Kurdish-dominated Syrian Democratic Forces called it the 'first blatant violation of Kurdish people's culture and history since the takeover of Afrin'.
A Turkish armed forces Twitter page posted a video of troops displaying the nation's flag in Afrin's centre.
Mohammad al-Hamadeen, spokesman for the Turkish-backed Free Syrian Army (FSA), said they met no resistance as they entered Afrin on three fronts.
'Maybe it will be cleared by the end of the day - it is empty of [YPG] fighters, they cleared out,' he said.
However, the British-based Syrian Observatory for Human Rights said Turkish and FSA fighters controlled around half of the city, with clashes continuing in some areas on Sunday morning.
Will Turkey press on?
President Erdogan has achieved his twin objectives: to remove a key area under YPG control and to rally the vast majority of Turks behind their commander-in-chief. The jingoism here has been breathtaking. Targeting Turkey's age-old enemy of the Kurdish militants is a rare uniting force in a polarised country. Those who have spoken out - several hundred - have been detained for 'terrorism propaganda'.
The question now is whether Turkey pushes on to other YPG-held areas, namely Manbij, which could put Turkish troops in direct conflict with US soldiers there who see the YPG as allies. That depends on talks between Ankara and Washington, and the sacking of Secretary of State Rex Tillerson last week removes an important interlocutor for Turkey.
The risk in Afrin is that many residents who will return are Kurdish and could see Turkey as the aggressor. Tearing down a Kurdish statue in the town centre doesn't augur well. Will the Afrin operation actually push more local people into the arms of the YPG?
Why has Turkey taken Afrin?
The Turkish assault on Afrin, named Operation Olive Branch, began on 20 January, with the aim of ridding the city and surrounding region of the YPG.
Turkey regards the YPG as an extension of the banned Kurdistan Workers' Party (PKK), which has fought for Kurdish autonomy in south-eastern Turkey for three decades.
The YPG denies any direct organisational links to the PKK - an assertion backed by the US, which is allied with the YPG in the battle against the jihadist group Islamic State (IS) in Syria.
US plans to help form a Kurdish border force set alarm bells ringing in Ankara, and prompted the launch of Operation Olive Branch.
President Erdogan vowed to 'suffocate' what he called a 'terror army.'
Turkey also announced plans to push Kurdish forces from Manbij, another city near the border.
What is the Free Syrian Army?
Backed by Turkey, the Free Syrian Army is a rebel group operating in the north of the country.
It is helping Turkey to secure its border with Syria, and has fought against the Syrian army, the Kurdish-led Syrian Democratic Forces and the Islamic State group.
What is happening elsewhere in Syria?
The assault in the north-west coincides with a Syrian and Russian offensive on Eastern Ghouta, an enclave near Damascus.
The Syrian army is pushing into the area with the support of Russian air strikes, and there are reports of civilian casualties.
The pro-government assault is said to have captured 70% of the enclave. Seizing it would be a major victory for President Assad.