Their first attempt was aborted after Syrian officials failed to deliver the toxic chemicals to the collection point in the Syrian port of Latakia.
Bad weather, shifting battle lines, and road closures were blamed for the missed 31 December deadline.
Removing the most toxic chemicals is the first step of a deal to eliminate Syria's chemical arsenal by mid-2014.
The Scandinavian fleet will sail from the Cypriot port of Limassol on Friday, reports a BBC's correspondent, who is travelling on board the Norwegian frigate.
Under the international disarmament plan, US satellites and Chinese surveillance cameras are to track the progress of Russian armoured lorries as they carry the chemical weapons from 12 storage sites in Syria to Latakia, on Syria's Mediterranean coast.
Danish and Norwegian cargo ships will then transport the chemicals to a port in Italy, where they will be loaded on to the US Maritime Administration vessel MV Cape Ray and taken out into international waters before being destroyed by hydrolysis.
The most dangerous ingredients include around 20 tonnes of the blister agent sulphur mustard.
The agreement on removing chemicals was brokered by the US and Russia after rockets filled with the nerve agent sarin were fired at three towns in the Ghouta agricultural belt around the capital Damascus on 21 August. Hundreds of people were killed in the attacks.
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