"They are all alive," witness Elias Makundi, who said he had accompanied a relative of the miners to the site of the accident.
"Thankfully no-one died in the accident, although some (of the survivors) look very weak."
Media showed pictures of the rescued men, covered in mud and being helped by rescue workers, or lying on the ground, wrapped in blankets, before being taken to hospital.
"We are continuing making them stable and put them under supervision. We hope that we will start discharging them tomorrow," Joseph Kisala, a medical official in the northwestern province of Geita, was quoted as saying in the Daily News.
The men -- 14 Tanzanians aged 19 to 33, and a Chinese national -- were trapped without food or water when a shaft in the Chinese-run mine collapsed. The incident happened on either Thursday or Friday, according to conflicting reports.
Tanzania is the fourth-largest African producer of gold and the precious metal is one of the country's main sources of foreign currency.
The collapse of mine shafts is frequent, with miners often lacking the tools and materials considered necessary to operate safely.
In November 2015, five miners were found alive after spending 41 days 100 metres underground after an infall at a mine near the town of Shinyanga, also in the northwest.
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