The storm's maximum sustained winds were clocked on Wednesday at 185 km per hour, down from a peak of 225 km per hour a day earlier before Florence was downgraded from a Category 4 on the five-step Saffir-Simpson scale of wind strength.
The NHC said the first tropical storm-force winds of at least 39 miles per hour (63 kph) would hit the region early on Thursday with the storm's centre reaching the coast Friday.
"Preparations to protect life and property should be rushed to completion", the agency says.
Duke Energy has around 4 million customers in North and SC, and says it could take several weeks to restore the electricity.
Georgia joined four other coastal states issuing an emergency declaration as the latest forecasts showed Florence dumping historic amounts of torrential rain on the southern state.
South Carolina Governor Henry McMaster ordered as many as one million residents of the state's eastern coast to leave their homes ahead of the storm's predicted arrival today.
Duke Energy officials say Florence will knock out power to an estimated 1 million to 3 million customers in North and SC.
With South Carolina's beach towns more in the bull's-eye because of the shifting forecast, OH vacationers Chris and Nicole Roland put off their departure from North Myrtle Beach to get the maximum amount of time on the sand. "Some areas will receive rain in feet instead of inches".
'Hurricane force winds, ' another added.
The ocean waters that Florence is travelling over are about 2.7 degrees (1.5 degrees Celsius) warmer than normal, McNoldy said. Its maximum sustained winds have dropped slightly to 110 miles per hour.
"A motion toward the northwest is forecast to begin by this afternoon and continue through Thursday", the hurricane center says.
WCNC-TV meteorologist Brad Panovich told WFAE Morning Edition host Marshall Terry that the shift of Florence means more rain for the Charlotte area. It may move a little north into Virginia or a little south into SC.
Maryland, though, could be spared the catastrophic flooding thought possible in recent days.