The storm has killed at least two people and cut power to more than 2 million utility customers across the South.
As of 5 a.m. ET Thursday, Zeta's center was near the state line in northern Alabama and Georgia, about 65 miles to the west of the Metro Atlanta area lashing parts of both states with winds gusting over 70 mph.
"On the forecast track, the center of Zeta will move across portions of the southeastern US this morning, across the Mid-Atlantic states this afternoon, and emerge over the western Atlantic by tonight, it said Thursday morning.
Zeta to keep tropical storm intensity
Zeta's fast advance means the system won't lose much energy, CNN meteorologist Michael Guy said. This will allow Zeta to keep tropical storm intensity with strong winds throughout its course to the Atlantic.
Zeta is expected to bring strong gusty winds, isolated tornadoes and heavy rain with the potential to produce flash flooding overnight.
Hurricane and storm surge warnings have been discontinued for all of Louisiana and the Mississippi coast, but coastal areas of Alabama have been warned the storm surge threat remains due to remnant winds left in the wake of the hurricane.
At least 32.7 million people from the Gulf Coast toward the Carolinas were under Tropical Storm warnings Thusday morning. The last time metro Atlanta was under such a warning was October 2018 as Hurricane Michael passed over the region.
Many of the outages were in Louisiana, where the first death attributed to Zeta was reported Wednesday.
Louisiana still recovering from earlier storms
A 55-year-old man was electrocuted by a downed power line, the Louisiana governor's office, citing the Orleans Parish coroner.
"STAY INSIDE: Can't stress enough how dangerous the roads are right now in #NOLA. Widespread downed trees & power lines. Also, many traffic lights are out. If you MUST drive tonight, be extremely cautious & treat intersections with lights out as four-way stops. #Zeta," she wrote.
The cause of death was not available.
Louisiana's Lafourche, St. Bernard and Terrebonne parishes issued curfews for Wednesday evening, according to authorities in each parish.
Officials in Jefferson and Terrebonne parishes had issued mandatory evacuation orders ahead of the storm for coastal areas and places outside major levees. In New Orleans, voluntary evacuations were called for similar areas.
Most of the evacuees have been displaced since August from Laura and have been spread among six hotels in New Orleans, the governor's office said.
Edwards said more than 1,500 National Guard members had been activated and more than 5,000 linemen are staged to begin recovery and power restoration efforts Thursday morning.
"It's going to be a rough evening for Louisiana, particular in the southeastern portion. I am confident that we are well prepared for this," Edwards said.
Alabama Gov. Kay Ivey declared a state of emergency Tuesday. On Wednesday, she asked residents to finish storm preparations quickly and warned that even the central part of the state could see tropical storm winds.
"I urge everyone to quickly finish your preparations this afternoon and stay off the roads tonight, if possible," Ivey said. "Zeta is gaining strength and will certainly give a punch to our state, and we all must be ready. Stay safe."
Before turning its path toward the US coast, Zeta struck the Yucatán Peninsula in Mexico on Monday night as a Category 1 hurricane.