They were arrested in September on hooliganism charges after a protest at an Arctic offshore oil rig.
Three other activists – Swiss national Marco Weber, Faiza Oulahsen from the Netherlands and American Peter Willcox – were also released from detention on Friday, bringing to 15 the number freed on bail.
Greenpeace also said it expected to pay bail for six more members of the Arctic 30, potentially resulting in the release of 26 of the group before the weekend.
It is unclear whether those released on bail will be allowed to leave the country
The environmental group has launched a global campaign putting pressure on the Russian government to let them go.
Mr Perrett is a tree surgeon and director of a community interest company which encourages and supports the use of renewable energy.
Friends said he went to the Arctic driven by his belief that there are ways to live on this planet without destroying it. Before he left, he said he was nervous, but not afraid of going on the trip.
‘Saga far from over’
The 30 were arrested during a protest against drilling in the Arctic and were initially held in Murmansk before being moved to St Petersburg.
They were initially charged with piracy but the authorities said this would be changed to hooliganism.
Greenpeace International Arctic campaigner Ben Ayliffe said: “This is a wonderful moment for Anthony and his family and friends. But this will only really be over when he and the others are able to go home.
“For now, we are allowing ourselves a sigh of relief, all the time remembering that those brave men and women are still charged with a crime they didn’t commit, and of course our friend Colin was refused bail. This saga is far from over.”