Beryl hit the southern United States on Monday morning as a category one hurricane, but it has since been downgraded to a tropical depression, BBC reported.
Officials warned of destructive winds, up to 15in (38cm) of rain and "life-threatening" storm surges.
More than 1,100 flights were cancelled at Houston's main airport on Monday, according to flightaware.com.
Some 2.6 million customers in Texas were without power as of Monday night, said poweroutage.us, with some outages also reported in Louisiana. The storm caused at least 10 deaths in the Caribbean.
Officials said seven people had died in Texas's Harris and Montgomery counties, while one more fatality was confirmed in neighboring Louisiana.
Houston is a low-lying coastal city, making it prone to flooding.
SD/PR