The Miami-based center defines a major hurricane as one with wind speed greater than 110 miles per hour (177 kph).
Gradual strengthening is forecast and Florence could become a hurricane again over the weekend.
The National Hurricane Center said the storm is about 1,640 miles east of the Windward Islands, which are in the West Indies.
The Navy said all ships in Virginia's coastal Hampton Roads area were preparing to leave port for open seas Monday.
"Accordingly, I am declaring a state of emergency so that we can begin to prepare state assets, and I encourage Virginians to monitor forecasts and make their own preparations now".
Florence could cause life-threatening surf and rip currents along parts of the U.S. East Coast this weekend as the storm swirls across the Atlantic.
Officials in North Carolina are already bracing for impact.
The coast can expect tropical storm-force winds as early as Wednesday night and likely Thursday morning, with the highest probability of winds in the Carolinas. Advisories warning of risky beach conditions or coastal flooding were in effect for parts of New Jersey, Delaware, Virginia, North Carolina, South Carolina, Georgia, and Florida. The storm was centered about 905 miles (1,457 kilometers) east-southeast of Bermuda and moving west at 8 mph (13 kph).
Virginia and North Carolina and SC already are on alert.
The three tropical systems - Florence, Isaac and Helene - come right before the Atlantic hurricane season hits its peak Monday.
"We are preparing for the worst, and of course hoping for the best", South Carolina Gov. Henry McMaster said, adding his declaration would allow state agencies to deploy assets quickly to the coast.
Unsafe hurricane expected to reach major storm status Monday.
It's moving westward at 13 miles per hour, with maximum-sustained winds of 60 miles per hour.
"State emergency management, transportation, health experts and others are making sure North Carolina is prepared for the storm, and I urge the public to review your emergency plans and gather your supplies now", the release quoted Cooper. On the forecast track, Helene will pass very close to the southern Cabo Verde Islands tonight and early Sunday.