Florence will turn into a major hurricane by Monday, according to The National Hurricane Centre’s 11am AST (4pm BST) weather advisory.
The latest forecast has said the storm’s winds have reached almost 75 mph (120 km/h), which means it is now at hurricane-strength.
Winds are travelling at 15 miles (30 km) from the centre.
By Thursday, Florence will then turn into an extremely dangerous major hurricane.
The southeastern US coast will be most at danger on Thursday, when Florence could be at Category 4 strength.
Before that, the centre of Florence will move over the southwestern Atlantic Ocean between Bermuda and the Bahamas on Tuesday and Wednesday.
At the moment, swells from Florence are affecting Bermuda and parts the US East Coast.
The swells are set to cause life-threatening surf and currents, so people are being warned to listen out for local weather updates.
AccuWeather Hurricane Expert Dan Kottlowski warned that Florence could even make landfall along the U.S. East Coast.
States of emergency have been declared in North Carolina, South Carolina and Virginia in preparation of extreme weather caused by the hurricane.
Florence could bring damaging winds, heavy rain and storm surge flooding.
However, the strength and orientation of an area of high pressure over the western Atlantic will determine Florence’s movement this week.
Florence was declared this season’s first major hurricane after it quickly developed into Category 3 strength last Wednesday.
However, the hurricane was soon downgraded to a tropical storm after its winds rapidly weakened down to 70 mph.
At least 67 named storms have passed within 200 nautical miles of where Florence has been travelling since 1851.
So far, none of these storms have ever hit the US.
Florence is being steered by an unusually strong area of high pressure over the north Atlantic Ocean, which explains why it is heading that way.