Emergency protective measures, including direct federal assistance, will be provided at 75 percent federal funding, the White House said.
"President Trump and his administration executed swift and decisive action in approving our Federal Disaster Declaration", said Gov. Edwards.
The NWS placed Calcasieu and Cameron parishes under a tornado watch until 2 a.m. Monday.
National Weather Service has issued a flash flood watch until 7 p.m. Monday for Acadia, Allen, Beauregard, and Vernon parishes.
The weather service does not believe the storm will re-enter the Gulf of Mexico and come to southern Louisiana, but Edwards said residents should remain vigilant.
Marshall, Iberia Parish director of Homeland Security and Emergency Preparedness said the hurricane storm will be downgraded to tropical storm status this afternoon.
"It is critically important for the people of Louisiana, particularly those in southwest Louisiana, to recognize that we are not out of the woods", he added.
The estimated storm surge remains 1 to 3 feet above ground level for coastal sections of Southwest Louisiana and Southeast Texas.
South-central Louisiana was devastated by an unnamed flood in August 2016, which Edwards called the "third largest disaster in the country's history".
In Texas, at least two people are dead and more than a dozen injured due to the storm that has battered the region, including the cities of Corpus Christi and Houston.
Parts of Louisiana could get as much as 25 inches of rain, the Times-Picayune reported Sunday.
Days of rain swallowed thousands of roads and buildings in water throughout Louisiana.
In his Sunday statement, the governor also evoked Hurricane Katrina, which made landfall 12 years ago Tuesday, while pledging to help Texas through the storm.
Meteorologist Jared Rackley says they have yet to survey the area but photos show an overturned camper and other damage. "We will do nothing less to support to the people of Texas in any way that we can as they respond and recover from Hurricane Harvey".