Gustav flooded some low-lying areas where it made landfall on Monday
The mayor of New Orleans has lifted the evacuation order imposed on the city because of Hurricane Gustav, more than 12 hours earlier than planned.
The announcement means nearly 200,000 residents can begin returning home, although Mayor Ray Nagin warned that many services had not been restored.
On Monday, the worst of the storm missed New Orleans - the city ravaged by Hurricane Katrina in 2005.
President Bush flew over Louisiana on Wednesday to assess the damage.
Mr Bush, who missed the Republican Party convention in Minnesota to visit Louisiana, said that there was still a risk even after the storm and that residents should "listen closely to local officials and follow their instructions".
New Orleans will officially reopen at midnight local time (0400GMT) but Mr Nagin said that anyone who "jumped the gun" and arrived early would be allowed into the city.
But he warned returning residents that some city areas were still without power, the sewage system was damaged and hospitals had only skeleton crews.
The exodus was the largest evacuation in state history - with an estimated two million people fleeing the storm.
Gustav weakened rapidly after moving inland from the Gulf coast but still caused major damage to the state of Louisiana.
US officials reported eight storm-related deaths, according to the Associated Press news agency, adding to the 90 people Gustav killed across the Caribbean.
Separately, tropical storm Hanna has hit the Caribbean, causing heavy floods in the Bahamas, Cuba, Puerto Rico and Haiti.
In Haiti, at least 19 people were killed, officials say.
Mr Bush was due to visit Baton Rouge, one of the worst affected areas in the state of Louisiana.
David Paulison, head of the US Federal Emergency Management Agency (Fema), said Baton Rouge was hit "pretty hard" and was without power.
"We would caution people not to move back in until their parish president says it's safe to move back in," he said.
"Most of the areas don't have electricity. Some of them don't have water and there's no infrastructure in place - no grocery stores, gas stations - those type of things."
Mr Nagin said that New Orleans residents would be allowed to pass through the roadblocks put in place during the evacuation order.
"The message is: we want you to come into the city, check on your property, make sure that you are comfortable and make an intelligent decision on whether you want to stay in this environment or not," the mayor said.
He warned that New Orleans was still in a "vulnerable state" and that a dusk-to-dawn curfew would remain in effect for some time.
The city's rebuilt levees appear to have held back surging floodwaters.
Only 10,000 of New Orleans's population of some 200,000 remained in the city.
In 2005, three-quarters of New Orleans was flooded by a storm surge that claimed more than 1,800 lives in coastal areas.