"Because they never thought they would come into Russia they didn't have Russian visas, so they need some paperwork to enable them to leave the country," a Greenpeace NZ spokesman said.
"Our lawyers tell us it should be sorted out within the next few days. We're not anticipating any problems with that."
The two Kiwis in the group - David Haussmann and Jon Beauchamp - are "very keen to get home", the spokesman said. "Overall it's kind of a mixture of relief and an urgency to get home and spend time with their loved ones."
In a statement, Arctic Sunrise skipper Peter Willcox said: "This is the day we've been waiting for since our ship was boarded by armed commandos more than three months ago.
"I'm pleased and relieved the charges have been dropped, but we should not have been charged at all."
The Arctic 30 have been living in a St Petersburg hotel since being granted bail nearly five weeks ago.
They were freed under an amnesty that also saw two members of the punk band Pussy Riot released this week.