As much as 8 inches (20 centimetres) of rain could fall in some parts of the Gulf states through late Thursday.
A hurricane warning is in effect for the area stretching from the mouth of the Pearl River in MS to the Alabama-Florida border.
"On the forecast track, the center of Gordon will move across the northern Gulf of Mexico [on Tuesday], and will approach the north-central Gulf Coast within the hurricane warning area late [Tuesday] afternoon or evening, and move inland over the lower Mississippi Valley tonight and early Wednesday", the NHC said.
Sustained winds of tropical-storm-force are likely in the zone under a hurricane warning, with the possibility of hurricane-force gusts, over 74 miles per hour.
Florence was moving toward the west-northwest near 14 miles per hour and maximum sustained winds of 70 miles per hour with higher gusts.
The forecast now calls for Gordon to become a Category 1 Hurricane as it makes landfall along the Gulf.
New Orleans Mayor LaToya Cantrell says the city has "the pumps and the power" needed to protect residents from Tropical Storm Gordon.
Authorities across the Gulf Coast urged people to stay out of the water - warnings that beach lovers like Cameron Armstrong and Matthew Ewbanks ignored on their visit to Gulf Shores on the Alabama Gulf Coast. Rain and the flash flooding that can cause are the main threats expected from Gordon along with strong wind and storm surge.
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The storm began as a tropical wave over the Caribbean last week.
The National Hurricane Centre is also tracking Tropical Storm Olivia and Hurricane Norman in the eastern Pacific.
Geo Rodriguez chose to go for a walk on Hollywood Beach, north of Miami, on Monday morning and got caught in the storm. A voluntary evacuation was requested for areas that are outside levee protection.
The weather will gradually improve Wednesday.
A storm surge warning was in effect for the area between Shell Beach, Louisiana, and Dauphin Island, Alabama, with predicted heights of up to 3-5 ft if the peak surge coincides with high tide.
The National Weather Service said conditions were "possible" for tornadoes in the affected parts of South Florida on Monday night.
Tropical Storm Gordon has formed becoming the seventh named storm of the 2018 Hurricane Season. There are no coastal watches or warnings in effect.