Nato's International Security Assitance Force said that the Afghan National Army entered the town early on Monday.
Taliban fighters were reported to be abandoning Musa Qala as the troops arrived.
"The ANA [Afghan National Army] have entered the district centre. They are in the centre of the town," Major Charles Anthony, Nato spokesman, said.
Al Jazeera's Owen Fay said that Taliban fighters were leaving in an attempt to draw Nato and Afghan forces into a bigger fight outside the town.
"The senior Taliban commander in Musa Qala has told Al Jazeera that he has ordered his forces in a radical new deployment where they are ceding their control of the centre of Musa Qala," he said.
"He is then trying to broaden the fight to the outskirts, to the surrounding areas where those Afghan and British forces are fighting."
Fay said that the Taliban had claimed that as many as 4,000 of their fighters were being redeployed to the outskirts of the town in Helmand province.
General Mohammad Zahir Azimi, Afghan defence ministry spokesman, said that the Afghan, British and US troops had "completely captured" Musa Qala, however this was not confirmed by Nato.
Thousands of Afghan army and Isaf troops, along with about 200 to 300 US soldiers from the separate US-led coalition are deployed in the operation.
"The plan at this stage is for the Afghan forces, once Musa Qala is secure, to move in themselves to make sure that the Taliban cannot return and once again take power," Fay said from the Afghan capital Kabul.
Lieutenant Colonel Richard Eaton, a British military spokesman in Helmand, said the offensive was continuing as planned.
"I think it is going to continue today and overnight and I expect for tomorrow," he said.
Fighting around Musa Qala has stepped up since early November and the operation on the town started on Friday.
Taliban forces took the town in February, although the surrounding provincial areas are considered to be under Nato and Afghan control.
Two Nato soldiers and more than one dozen Taliban are reported to have died in fighting since Friday.
Yousuf Ahmadi, a Taliban spokesman, said that five Taliban had been killed, but that a "big number" of Afghan and foreign troops had also died. This was unconfirmed by Nato.
Meanwhile, Gordon Brown, Britain's prime minister, arrived in Afghanistan, visiting soldiers in Helmand province before travelling to Kabul.
"I thank every one of you for what you have done in what is the frontline against the Taliban because this is one of the most challenging of environments," he told the troops.
"To win here and to defeat the Taliban and to make sure that we can give strength to the new democracy in Afghanistan is important in defeating terrorism all around the world."
Brown, on his first trip to Afghanistan as prime minister, was due to hold talks with Hamid Karzai, the Afghan president, later on Monday, officials said.
Güncelleme Tarihi: 10 Aralık 2007, 23:38