"The Norwegian-Danish task group to transport Syria's chemical agents to destruction left the port of Limassol this morning," said Norwegian armed forces spokesman Lars Magne Hovtun.
"The four ships have now set a course toward a holding area in international water outside Syria, so we are most ready to enter the port of Latakia when the order arrives," he added.
The ships are to be joined by Chinese and Russian vessels inside Syrian waters under a plan agreed in Moscow today.
The year-end deadline for the removal of key weapons components was the first major milestone under a UN Security Council-backed deal arranged by Russia and the United States that aims to eliminate all of Syria's chemical arms by the middle of this year.
Syria's worsening civil war, logistical problems and bad weather had held up the operation to move chemical agents to the port of Latakia, said the joint UN-Organisation for the Prohibition of Chemical Weapons mission overseeing the operation.