Tropical-storm-force winds extend outward up to 105 miles [165 km] from the center.
"The fourth named storm of the hurricane season, Dorian, strengthened Wednesday into a hurricane near the U.S".
Dorian is expected to dump 3 to 5 inches (8-13 cm) of rain on Florida when it reaches the southeastern USA state, the NHC said.
Meanwhile, a second tropical storm has now formed about 265 miles southeast of Cape Hatteras, the hurricane center said.
"We are grateful that it wasn't a stronger storm", he told the Associated Press.
Winds in the 5- to 30-mph range could move into Georgia and the Carolinas as early as 8 p.m. Saturday, hurricane forecasters say. Tropical Storm and Hurricane Watches are expected to be issued over the next 24 hours.
The National Hurricane Center says Hurricane Dorian could potentially hit the US coast as a powerful Category 4 storm.
In the British Virgin Islands, Gov. Augustus Jaspert said crews were already clearing roads and inspecting infrastructure by late Wednesday afternoon.
Original forecasts had the storm ripping through parts of Cuba, the Dominican Republic, and the US and British Virgin Islands. But first, it's going to dump torrential rains on Puerto Rico, following a shift of the storm's center overnight.
Dorian's wind speeds won't approach those of Maria, the Category 4 storm that left more than 2,900 people dead in Puerto Rico.
Wednesday's projections come five days before Dorian could reach parts of the mainland on Monday. "When they do, let them know it, and give them a big Thank You - Not like last time", Trump tweeted. The island's 3.2 million inhabitants still depend on a shaky power grid that has remained prone to outages since it was destroyed by the Category 4 storm.
Libby says some areas could see more than 100 millimetres before the rain ends Friday morning.
The centre said that a tropical storm watch remains in effect for the Dominican Republic from Isla Saona to Samana.
Tropical Storm Erin isn't a threat to the U.S.