"The submarine resurfaced and the seven submariners are alive," Russian navy spokesman Igor Dygalo said.
"They emerged by themselves, transferred to a motor-launch and will be placed aboard a ship where they will receive medical treatment," Dygalo said.
Once back on land, the crew were expected to be taken to a local hospital in Petropavlovsk-Kamchatsky for observation and medical care.
Rear Admiral Vladimir Pepelyayev, deputy chief of the Russian naval general staff, described the condition of the crew as "satisfactory".
The Priz AS-28 made an emergency surfacing and appeared on the water at around 4.26pm local time on Sunday, said a Russian naval spokesman.
Naval officials had been in regular contact with the crew, who faced dwindling oxygen and chilly temperatures.
Earlier a British remote-controlled vehicle on Sunday cut away the cables that had snarled the mini-submarine and its seven-man crew deep under the Pacific Ocean.
Race against time
US and British navies aided the
With oxygen supplies dwindling after nearly three days underwater, rescuers had been racing to try and bring the 13.2-m-long vessel to the surface at the site in Beryozovaya Bay, about 15km off Kamchatka's east coast.
Russian ships had earlier managed to loop cables under the antenna that snared the ship on Thursday.
Russian authorities had been hoping to avoid losing a sub crew as they did with the Kursk nuclear submarine, which sank almost five years ago, killing all 118 on board.
Russian estimates of how long the air would last had ranged from the end of Saturday to Monday.
In sharp contrast to the August 2000 Kursk disaster, when the authorities held off asking for help until hope was nearly exhausted, Russian military officials quickly sought help from US and British authorities.
Officials said the Russian submarine was participating in a combat training exercise and got snarled on an underwater antenna assembly that is part of a coastal monitoring system. The system is anchored with a weight of about 60 metric tonnes, according to news reports.
Russia's cash-strapped navy apparently lacks rescue vehicles capable of operating at the depth where the sub was stranded, and officials say it was too deep for divers to reach or the crew to swim out on their own.
Vows of better navy equipment by
Putin have apparently not helped
An earlier attempt to drag the vessel to shallower waters failed when cables detached after pulling it some 60m.
The new crisis indicated that promises by President Vladimir Putin to improve the navy's equipment apparently have had little effect. He was sharply criticised for his slow response to the Kursk crisis and reluctance to accept foreign assistance.
By early Sunday, Putin had made no public comment on the latest sinking.
Russian Defence Minister Sergei Ivanov, dispatched on Saturday to oversee the rescue operation, arrived at the scene just in time to monitor the quick progress made by the British robot in cutting the stricken submarine free.
"I want to thank our English colleagues for their help in the
rescue operation," Interfax quoted Pepelyayev as saying.