"The transit to Italy is expected to take several days," Pentagon spokesman Rear Admiral John Kirby said in a statement.
Once the weapons and chemical materials are on board, the Cape Ray will head "for international waters to begin neutralization of the chemical agents" at sea, he added.
Syria has shipped out 1,300 tons of chemical agents. Only the most dangerous elements - dubbed "priority 1" and used in mustard gas and Sarin - will be destroyed on board the US ship.
There are about 700 tons in this category, US undersecretary of defense Frank Kendall has said.
The Pentagon said at the beginning of the year that the process to destroy the agents and materials will take between 45 and 90 days.
The Cape Ray has been equipped with two Field Deployable Hydrolysis Systems - portable treatment plants capable of "neutralizing" the most dangerous Syrian chemical agents.
The process should destroy more than 99 percent of the chemicals, reducing the lethal agents into a sludge similar to low-level hazardous industrial waste.
Private waste treatment facilities will handle the disposal of that sludge.
Destroying chemical agents at sea will be a first, but the technology has been around for decades, according to Adam Baker, a chemical engineer with the US military's Edgewood Chemical Biological Center.