Cheers broke out among relatives at the news
Bells at a church in the state of West Virginia where relatives had gathered rang out with the news just before midnight on Tuesday (0500GMT).
Earlier, state governor Joe Manchin said it would take nothing short of a miracle to save the men.
The news came a few hours after the body of one man was found near the site of the explosion.
Officials said the man who died, who has not yet been identified, appeared to have been dropped off in a mine car by his colleagues and was close to the explosion site.
The 12 miners are thought to been further down the mine, more than 200ft (61m) underground, at the time of the blast.
Toxic gas
Kay Weaver, whose brother-in-law Jack Weaver was in the mine, said family members learned of the rescue when a man burst into church, shouting: "It's a miracle, it's a miracle!".
"They told us they have 12 alive," Gov Manchin said.
The miners "are being moved to the surface, and their condition is being assessed while they are being moved", his spokesman Tom Hunter said.
Relatives and friends cried and embraced each other at the news. Emergency vehicles and ambulances were at the scene. A local hospital was on high alert.
It has been a long wait for news
There had been no communication with the men in the Sago mine since Monday morning, and there are no reports on their condition.
Television reports say the men will be reunited with their families at the church in a few hours.
Officials had expressed concern at dangerously high levels of carbon monoxide underground.
The miners had with them a day's worth of food and water supplies, and were equipped with individual air purifying systems that would give them up to seven hours of clean air, officials had said.
Mining company head Ben Hatfield said earlier that there was a chance the miners had managed to take shelter from the toxic gas levels, after their mine car was found empty.
The cause of the blast is unclear.
Localização do estado da Virgínia.


12 mineiros  foram encontrados mortos e houve um sobrevivente no interior de uma mina de carvão, em Sago, no estado americano da  Virginia. 

Notícia divulgada pela imprensa anteriormente fôra  que 12 mineiros tinham sobrevivido e que apenas um morrera, o que fez com que familiares dos supostos sobreviventes comemorassem.

Na Igreja Batista de Sago, o presidente da companhia mineradora, a ''International Coal Company'', retificou a informação errada e avisou as famílias sobre os 12 mineiros mortos.  Ele atribuiu o falso comunicado   à falta de comunicação. Os familiares acusaram  o executivo   de ter "mentido" para eles. 

O nome do único minerador sobrevivente é Randal McCloy. Ele continua internado no  ''Ruby Memorial Hospital''.

Por volta das 6h40 da segunda-feira (2),  13 mineradores ficaram presos   cerca de 3 km dentro de uma mina de carvão, em Sago, Virgínia,   depois de uma explosão de metano.