The city was once the Taliban's stronghold, and is strategically important as a leading trade hub.
"Following heavy clashes late last night the Taliban took control of Kandahar city," a local government official told Reuters news agency.
Kandahar is the latest city to fall, after Herat and Ghazni on Thursday.
Meanwhile, the United States said it is sending nearly 3,000 troops back into Afghanistan to help evacuate staff from the American embassy.
The US said it was sending troops to the airport in Kabul to help evacuate a "significant" number of embassy staff on special flights.
The UK said it was also deploying about 600 troops on a short-term basis to provide support to British nationals leaving the country. The number of staff working at the British embassy in Kabul has been reduced to a core team.
The insurgents have moved quickly, seizing new territories as US and other foreign troops withdraw after 20 years of military operations.
Within hours of each other on Thursday some of Afghanistan's most important cities were captured - Herat, Ghazni and Qala-I-Naw came under Taliban control.
A Taliban spokesman also announced that "Kandahar is completely conquered".