Dorian made landfall in the Bahamas as a Category 5 hurricane with sustained winds of 185 m.p.h. and gusts over 220 m.p.h., according to the National Hurricane Centre (NHC).
A category 5 hurricane is considered to have had sustained wind speeds greater than 157 mph (252 km/h).
Officials also warm a storm surge could be life-threatening and as high as 23ft (7m) in places. The storm made landfall at 12:40 at Elbow Bay, the NHC said.
After hitting the Bahamas, it should move closer to the Florida east coast late on Monday through Tuesday night local time.
The Prime Minister of the Bahamas, Hubert Minnis, announced an evacuation order for parts of Grand Bahama and the Abaco Islands, both in the north of the archipelago. All tourists were asked to leave the islands. At a news conference, Mr Minnis begged residents to head for the main island to escape the “devastating, dangerous storm”.
Dorian’s exact path remains uncertain but a state of emergency has been declared in four US states: Florida, Georgia, South Carolina and North Carolina.
Florida was earlier expected to take a direct hit in the storm. Its governor, Ron DeSantis, has activated 2,500 National Guard troops and has another 1,500 on standby.
Hurricanes, which vary in strength from category one to five on the Saffir-Simpson scale, tend to get stronger as they move over warm waters like those off the coast of Florida.
Category five hurricanes, are relatively rare, although four other storms – Michael, Maria, Irma and Matthew – reached this level in the last three years.
Dorian has also grown larger in size, with hurricane-force winds currently extending 45 miles (75km) from the storm’s centre.