The 30 activists on board Greenpeace's Arctic Sunrise ship were detained on Sept 19 by the Russian authorities after attempting to stage a protest against oil drilling at Prirazlomnaya platform in the Pechora Sea.
On receipt of the bail, the crew and the ship should be allowed to leave Russia, said Judge Shunji Yanai.
The tribunal declared that the Greenpeace crew should not suffer from a dispute between countries. The Netherlands would have to pay the security deposit in the form of a bank guarantee.
Last month, the Netherlands asked the tribunal to order the release of the detained activists.
Dutch media reported on Friday that two Dutch crew members were released from prison in St. Petersburg after they had been granted bail by a Russian court on Wednesday.
The Netherlands took action because the ship sails under a Dutch flag.
The Hamburg tribunal was established by the 1982 UN Convention on the Law of the Sea. Both the Netherlands and Russia are signatories.
However, in response to the ruling, the Russian foreign ministry said that the Greenpeace case does not fall under the jurisdiction of the tribunal, according to media reports.
Russia earlier accused the activists and their ship of posing a security threat.