Svitzer spokesman Patrick Adamson told RIA Novosti the ship and crew had been released, but gave no details on the ransom paid to the pirates.
International news agencies cited officials as saying $700,000 had been paid.
The Danish-owned vessel had four Russian crew members, a British captain, and an Irish engineer on board.
The pirates operating in Somalia's northern region of Puntland captured the Russian ship off the Horn of Africa and took the crew hostage during a voyage from St. Petersburg, around Africa, to Russia's Far Eastern island of Sakhalin, where it was intended for use in oil and natural gas projects.
The company that owns the tugboat - Svitzer Wijsmuller Sakhalin Ltd. - has been contracted by Sakhalin Energy, the operator of a vast oil and gas project off Sakhalin, to transport ships to the region.
Pirate attacks are a common occurrence off Somalia's coast, and in the past several vessels carrying United Nations aid to the country have been targeted. Attackers usually seize cargo, money and other valuables, but rarely capture ships or crew members.