The hurricane has been downgraded to a post-tropical cyclone but is still causing plenty of trouble in Canada. One video on Twitter showed a crane collapsing onto a building in Halifax due to the tropical winds.
The storm hit Canada at 7.15pm AST (12.15pm BST) on Saturday, making landfall near Sambro Creek in Nova Scotia.
The storm’s estimated sustained winds hit 100mph (155kmh) when it made landfall 15 miles (25km) south of Halifax, according to the National Hurricane Centre (NHC).
Currently, Dorian is heading northeast at 30mph.
Although the storm has been downgraded, it is still dangerous with sustained winds equivalent to a Category 2 hurricane.
Hurricane warnings remain in effect for parts of Nova Scotia and Newfoundland.
Earlier on Saturday, the storm transitioned from a hurricane to a post-tropical cyclone.
The storm lost its hurricane status because it lost its warm core, according to CNN’s meteorologist Gene Norman.
Mr Norman said: “While the change in classification is technical, the fact of the matter is it’s still a dangerous situation and people in the area should not let their guard down.”
Most of the power cuts were caused by high winds that downed trees and heavy rain.
The extreme conditions are likely to continue throughout the night.
The hurricane’s destructive path has lasted two weeks and has unleashed devastation in the Bahamas, leaving 43 people dead.
In the US, several cities were left cleaning up after it made landfall in Cape Hatteras, North Carolina.
There have been five reported deaths in the US caused by Dorian so far.
The main concern in New England is the high surf as the storms move out.
CNN meteorologist Robert Shackelford said: “Some areas can see 18 to 20 feet breaking waves, so even the strongest swimmers are warned to be cautious of high waves.
“Swimmers are also advised to be cautious of rip currents, which can rapidly pull swimmers out to deeper waters.”
Other areas on the east coast can also expect gusts of winds of up to 30mph throughout the day.
Nantucket Island in Massachusetts could see wind gusts of between 58mph (93kmh) and 73mph (117kmh).