The Gulf depression has strengthened into tropical storm Hanna, the National Hurricane Centre said on late Thursday.
Heavy rains are likely over portions of Texas this weekend, it added, where a tropical storm watch has been issued.
Hanna was bringing winds of 65 kilometres (40 miles) and was located about 620 kilometres (385 miles) east-southeast of Port O'Connor in Texas.
The NHC earlier warned that rains caused by the storm could result in flash flooding and minor river flooding in the area.