Koblyakov, a dual Russian and French citizen, founded the French NGO Russie-Libertés, which has staged anti-Putin protests in France.
He was arrested in Bulgaria on 29 July after Russia said it wanted him on fraud charges.
He denied any wrongdoing and a Sofia court rejected Russia’s request for his extradition on 21 October for lack of evidence.
The prosecution had the option of appealing the court ruling but did not file a protest by a Tuesday deadline so the court's denial of the extradition has come into effect, his lawyer Bilyana Kotsakova told AFP news agency.
"He is now free to leave the country," she added.
Koblyakov said he planned to return to France "in the coming days".
"This decision of the court shows that Bulgaria is a true member of the European community when respect for human rights is concerned," he said.
Criticism of Russia's campaign against dissent has grown as Moscow clamps down on activists, journalists and internet users.
Koblyakov's detention had sparked protests in Sofia and Paris where human-rights activists had urged the Bulgarian authorities to reject the extradition request.