A million people are without power in Louisiana from Hurricane Ida, which has been downgraded to a tropical storm.
Ida brought 150mph (240km/h) winds when it made landfall, leaving a trail of destruction through the state before passing into Mississippi.
However, the full scale of the destruction will only become clear as the day goes on, officials said.
"Daylight will bring horrific images as the damage is assessed", tweeted Shauna Sanford, communications director for the Louisiana Governor.
President Joe Biden had previously said Ida would be "life-threatening", with the National Hurricane Center warning that heavy rain could still cause flooding in parts of the state.
But it seemed that New Orleans' flood defences, strengthened after Hurricane Katrina killed 1,800 people in 2005, have so far done their job. Mr Edwards said the levees had "for the most part" held - although the storm surge, rain and wind had still had a "devastating" impact across the state.
The president has declared a major disaster in the state, releasing extra funds for rescue and recovery efforts.
Ida gathered strength over the warm waters of the Gulf of Mexico during the weekend. More than 90% of oil production there has been shut down as a result of the storm.
On Sunday, Ida made landfall south of New Orleans as a category four hurricane - meaning it would cause severe damage to buildings, trees and power lines. As it moves inland, Ida's winds have dropped to 95mph (153km/h), meaning it is now a category one storm.
There are still fears of storm surges along the coast - which could be as high as 16ft (4.8m), potentially submerging parts of the low-lying coastline.