The rescue, about 75 hours after the Priz AS-28 mini-sub became snagged 190 metres underwater during military exercises, was completed with just hours of oxygen supplies left for the stranded crew.
“We believed the whole time that we would be saved,” the sub’s captain, Vyacheslav Milashevsky, told ITAR-TASS news agency after reaching the regional capital, Petropavlovsk-Kamchatsky, by boat.
The men, wearing naval uniforms, looked drained, but happy as they stepped onto dry land.
“I cried from happiness and danced,” Mr Milashevsky’s wife Yelena said on state-run television.
The sailors were pronounced in good health and taken to hospital for further check-ups.
The key to the submariners’ rescue, 70 km off Petropavlovsk-Kamchatsky, was the arrival of a British navy team with a sophisticated Scorpio underwater robot.
In a six hour operation using powerful cutters, the Scorpio slashed through the cables of a coastal defence antenna and fishing nets which had entrapped the sub.
Defence Minister Sergei Ivanov, who arrived just as the British team was going to work, was shown on national television cheering from a ship at the scene.
The British rescue came after two days of futile efforts by Russian ships to haul up the mini-sub.
“The rescue operation has had a happy ending. I thank everyone, including of course the British rescuers,” Pacific fleet commander Admiral Viktor Fyodorov said.
British naval Commander Jonty Powis said the mission was a close shave.
“We were conscious that the crew were running out of oxygen and that we could not afford any great delays in cutting them free,” he said.
President Vladimir Putin ordered an official inquiry and issued a statement expressing thanks to rescuers.
Five years ago 118 Russian sailors perished on the sunken nuclear submarine Kursk.
The accident site was in a militarily sensitive area off the Kamchatka Peninsula, underlined by the fact the mini-submarine was caught up in one of Russia’s own underwater coastal defence antennas.