The National Hurricane Center says Edouard has been downgraded to a tropical depression as it moves inland across eastern Texas and western Louisiana.
Coastal tropical storm warnings were canceled after Edouard made landfall Tuesday morning east of Galveston.
The storm kicked up heavy surf and drenched tourists visiting during the height of the summer season, but there were no reports of major damage or flooding.
On Tuesday afternoon the storm's center was about 35 miles north-northeast of Houston, moving about 9 mph with 35-mph sustained winds.
Forecasters say the storm's remnants could produce 3 to 5 inches of rain across eastern Texas and Louisiana, with up to 10 inches possible in isolated spots.
They also warned that it could produce spinoff tornadoes.
Though forecasters had feared it could become a hurricane and both Texas and Louisiana had made emergency preparations, winds never reached hurricane strength of 74 mph. No major damage was reported.
Edouard skirted the Louisiana coast on its way to Texas, raising tides and pushing water into bayous and yards. Residents of low-lying areas south of the Intracoastal Waterway in Cameron were ordered to evacuate Monday but were expected to be able to return later Tuesday. Parish officials have been quick to order evacuations ahead of storms since Hurricane Audrey in 1957 killed about 500 people in Cameron.
Houston's two major airports, Hobby and Bush International, were operating Tuesday morning, though flights were delayed anywhere from 30 minutes to five hours.
The storm hit at the height of tourist season in Galveston, but Edouard did not bring the 100-mph winds that punished the Texas tourist hotspot of South Padre Island when Hurricane Dolly tore off roofs and knocked down signs last month July 23.
The Texas coast counts on tourism this time of year. About 50 million visitors to the Texas coast spent about $15 billion in 2006.
Since Dolly, South Padre has regained electric power but its four biggest full-service hotels remain closed as well as the convention center in the community about 260 miles down the coast from Galveston.
Edouard did prompt offshore oil and gas companies to evacuate a few of the 717 manned platforms and 125 operating rigs in the Gulf.
But Shell Oil Co. said the storm had no effect on its offshore operations and it would begin returning evacuated workers Tuesday.