The ship has 13 sailors, including 11 Russians, on board.
The CEC Future ship, which is operated by Danish Clipper Group company, and its crew members had been held off the Somali coast since early November before being released on Thursday after a ransom, believed to be up to $2 million, was paid.
"The Fotiy Krylov salvage tug with a unit of naval infantry on board is escorting the Future ship from the port of Salala to Oman," Captain 1st Rank Roman Martov said.
In Oman, the sailors will receive medical assistance and the Russians will be flown home, the official said.
The Fotiy Krylov arrived in the Gulf of Aden in early January as part of a naval task force from Russia's Pacific Fleet, led by the Admiral Vinogradov missile destroyer.
The Admiral Vinogradov, which has replaced the Neustrashimy (Fearless) frigate from the Baltic Fleet on an anti-piracy mission off the Horn of Africa, is currently escorting two tankers under the Russian flag along the Somali coast and its helicopter is conducting maritime reconnaissance over the area.
The Russian military said earlier on Friday that Russia had sent two Black Sea Fleet vessels to take part in an anti-piracy operation in the Gulf of Aden.
Pirates have been increasingly active in the waters off Somalia, where over 110 ships were attacked in 2008, with 42 vessels seized and 815 crew members abducted. Up to 20 warships from the navies of at least 10 countries are involved in anti-piracy operations off the coast of the lawless East African nation.
