The storm triggered hurricane warnings stretching from High Island, Texas, to Morgan City, Louisiana.
As the 10th named storm to strike the continental US this year, Delta's arrival snapped a century-old record.
Hurricane Delta is the 25th-named storm this year.
Oil explorers, tugboat operators and other U.S. Gulf Coast businesses got back to work on Saturday after the region was slammed by its second hurricane in six weeks.
Many people left their homes to try to get out of the storm's path. He had gathered food, plenty of water and had covered his windows to protect against flying debris during Delta.
In Galveston, Texas, about 100 miles (160 kilometres) from where the centre made landfall, winds toppled trees, street signs and two homes under construction, and with dunes flattened by earlier storms, the surge reached beneath raised houses.
The Hurricane Center said wind gusts in Lake Arthur, Louisiana, reached 96 miles per hour (154 kph) as Delta made landfall.
Residents in parts of the U.S. state of Louisiana jammed highways as Hurricane Delta spun across the Gulf of Mexico toward a region struggling to recover from the damage inflicted by a hurricane less than two months ago.
"I just didn't want to leave".
Continued weakening is forecast to occur, and Delta should become a tropical storm, and then a tropical depression, on Saturday.
"The last one was the worst one, this one can not be worse", said Olmsted, who works for an electrical utility and lives with her boyfriend. "I just put it in the Lord's hands", Jack said, pointing skyward. Tropical Storm Beta also hit Texas last month, wreaking destruction across parts of the state's coast. Further east, in Acadiana region towns like New Iberia and Abbeville, people took the storm seriously.
The station said photos of crushed cars and damaged homes were widespread, as well.
Laura damaged about 95% of the homes and buildings in Lake Charles, and up to 8,000 residents continue to live in temporary housing.
By 7am (local time), Delta was centered near the Louisiana-Mississippi state line and barely a tropical storm.
New Orleans may be spared the worst of the storm, although it will be hit by gusty winds and mild rain, said AccuWeather meteorologist Dan Kottlowski, with Lafayette the largest city on the storm's eastern and more risky side.
"They never had time to recover from Laura and now this next storm is hitting them".
Louisiana Gov. John Bel Edwards said President Donald Trump approved his request to declare a federal emergency, which frees up federal resources.
The remnants of Delta exit the area Monday night. We could see the chance for localized flooding in some spots, along with a chance of flash flooding on roadways.
The Louisiana governor's office said it had no reports of deaths early Saturday, but a hurricane's wake can be treacherous.
Having crossed the Gulf of Mexico, Delta is now moving across central and north-eastern Louisiana, and will enter northern MS and the Tennessee Valley on Saturday.
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