Police say the driver lost control and the bus rolled over on Highway 83 about 46 miles (74km) north of Laredo. No other vehicle was involved.
Seven people died at the scene and one other died later in hospital. The driver was among the survivors.
Police said the cause of the crash was being investigated.
The coach, carrying 51 passengers, belonged to OGA Charters and had been travelling to a casino in Eagle Pass, about 125 miles north-west of Laredo, the Laredo Morning Times reports.
Texan Governor Greg Abbott issued a statement expressing his condolences, the report added.
Trooper Conrad Hein, of the Texas Department of Public Safety, said: "Our troopers are going to look into what happened, but it's going to take us some time."
He said rain had affected the area on Saturday morning but it was unclear if that was a factor.