As Ankara said its allies now had "near complete control", the rebel announcement came on the opening day of peace talks between the Syrian opposition and regime in Geneva.
Al-Bab, just 25 kilometres (15 miles) south of the Turkish border, was the last IS stronghold in the northern Syrian province of Aleppo.
"We are announcing Al-Bab completely liberated, and we are now clearing mines from the residential neighbourhoods," said Ahmad Othman, a rebel commander.
"After hours of fighting, we chased out the last remaining IS rank and file that were collapsing after the fierce shelling of their positions," he added.
Turkish Defence Minister Fikri Isik said rebels had "near complete control" of Al-Bab.
"When the search and combing operations are over, we will be able to say that Al-Bab has been completely cleared of Daesh (IS) elements," he said, quoted by state-run Anadolu Agency.
- 'Tall task' ahead -
Isik reaffirmed that Turkey was now ready to join any operation by international coalition forces to take the Syrian city of Raqa, the extremist group's de-facto capital.
Anadolu had earlier reported that rebels had surrounded the town to "break" IS's will but had held off on storming the centre "with the aim of preventing civilian casualties".
The Syrian Observatory for Human Rights, however, said IS fighters were still present in parts of the town and that rebels were in control of less than half of it.
Rebels launched an offensive to capture Al-Bab last year with the support of Turkish ground troops, artillery and air strikes.
Al-Bab was IS's last remaining stronghold in Aleppo province, after a US-backed alliance of Kurdish and Arab fighters seized the town of Manbij in August.
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The jihadist group still controls a scattering of smaller villages and towns in the province.
Field commanders from two other rebel factions in the town also claimed the capture of Al-Bab to AFP.
"Yesterday (Wednesday), we captured the city centre, which was IS's security zone... The jihadists collapsed, and this morning around 6 am (0400 GMT) we completed the operation," said Saif Abu Bakr, who heads the Al-Hamza rebel group.
Abu Jaafar, another rebel field commander, said he expected clearing up operations would be wrapped up within hours.
"Dozens of IS fighters were killed and we evacuated more than 50 families from inside Al-Bab," Abu Jaafar said.
Turkey sent troops into Syria in August last year in an operation it said targeted not only IS but also US-backed Kurdish fighters whom it regards as terrorists.
The battle for Al-Bab has been the bloodiest of the campaign with at least 69 Turkish soldiers killed there.
The town was also seen as a prize by Syrian President Bashar al-Assad's forces, who had advanced to just 1.5 kilometres (one mile) from Al-Bab in recent weeks.
"Al-Bab is important, insofar as its taking from IS will deprive the group of a tax base and an area where it was able to congregate and plot attacks against Syrians and the West," said Aaron Stein, a senior fellow at the US-based Atlantic Council.
"For Turkey, the mission, as was defined back in 2016, is now complete: Turkish forces have forced IS from the border and cut the overland route between the two Kurdish cantons" in northern Syria, he told AFP.
Syria's Kurds have managed autonomous administrations in swathes of the country's north since 2012, and Al-Bab falls between the "cantons" of Kobane and Afrin.
"However, Turkey will now have to grapple with the questions of prolonged occupation of a foreign country and help to oversee the transition to civilian rule, a tall task for any foreign military," Stein added.
More than 310,000 people have been killed since Syria's conflict broke out in March 2011 with protests against Assad that spiralled into all-out war.