The man has been identified as Anthony Perrett from Newport in Wales, who is now preparing to leave Russia.
He was in the group of 28 activists and two freelance journalists arrested in September as they staged a protest at a Russian offshore oil rig.
They were all charged with hooliganism – but have all been freed on bail.
They are being granted amnesty under a new Russian law which has seen several high-profile releases in recent days.
Greenpeace said on Tuesday that one man from the “Arctic 30” group had been told his case was now closed, and that others were expected to receive notice soon.
The statement did not name the man.
An earlier report saying that three people had been notified for release was later corrected.
Twenty-six of the group are foreigners – six of them Britons – and Greenpeace said they would be free to leave Russia once they had the right stamps in their passports.
“We know that getting those stamps would be the best Christmas present for the Arctic 30 and we hope it can happen quickly, but until such time as they do, we still cannot say when they will leave,” it said in a statement.
The detainees, from 16 different countries, had sailed to an oil rig operated by Russia’s state-run energy company Gazprom in September.
They were intercepted by Russian coastguards, who fired warning shots as some activists tried to climb on board the rig.
Their ship, the Arctic Sunrise, was seized.
The group was initially charged with piracy but the charges were later reduced to hooliganism.
They denied the charges, saying their protest had been peaceful and legal.
The Russian amnesty law was passed last week by the State Duma and could see the release of some 20,000 people.
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