A tropical storm warning was in place from Fernandina Beach in Florida to Altamaha Sound in Georgia.
It was expected to dump between 3 and 6 inches of rain on the northeast Florida, Georgia and parts of the South Carolina coastlines through Friday afternoon, forecasters said.
"Gradual weakening is forecast during the next day or so, and Julia is expected to weaken to a tropical depression later [Wednesday]," the NWS added.
Some isolated areas could get up to 10 inches of rain and flash floods are possible, the weather service said. Florida Gov. Rick Scott urged residents to review and evacuation plan just in case.
"We know that heavy rainfall is expected across northeastern Florida between Daytona Beach and the Florida - Georgia border for the next several days," Scott said.
He also urged residents to dump standing water in an effort to help control mosquitoes which can carry the Zika virus.
Parts of Florida were flooded last month when Hurricane Hermine struck the state's northwest Gull of Mexico coast. Two deaths, one in Florida and one in North Carolina, were blamed on the storm.