The storm, with maximum sustained winds of 85mph (137km/h), is moving north, and a second landfall is expected on the Mississippi coast later.
Louisiana, Mississippi, Alabama and parts of Florida have issued hurricane warnings and evacuation orders.
Nate killed at least 25 people in Nicaragua, Costa Rica and Honduras.
The tropical storm has since strengthened and is now a category one hurricane on the Saffir-Simpson scale.
Although not as strong as last month's Maria and Irma, Nate is expected to bring strong winds and storm surges.