The storm is expected to dump more than 90cm of rain
The strongest hurricane to hit the US in 12 years has weakened to a category 2 storm.
Hurricane Harvey was initially classed as a category 4 hurricane. However, winds are still reaching 100mph.
It landed on a stretch of coastline near the town of Rockport at around 4.00am Irish time bringing "life-threatening" winds of 130mph.
Power to some homes was knocked out, and signs and pieces of palm tree littered the streets as the storm took hold.
There are also reports of roofs collapsing into houses, trees being uprooted and buildings being destroyed.
A county sheriff's department has also warned the public to be on the look out for alligators, washed out of their creek habitats by the storm surge and seeking higher ground.
US President Donald Trump has signed a disaster proclamation as he faces his first major emergency as president.
The storm is expected to dump more than 90cm of rain along the Texas coast and parts of Louisiana over several days.
Harvey has been compared to one of America's deadliest storms - Hurricane Katrina - which killed more than a thousand people in New Orleans in 2005. New Orleans does not lie in Harvey's direct path.
President Trump wrote on Twitter: "At the request of the Governor of Texas, I have signed the Disaster Proclamation, which unleashes the full force of government help!"
The president is currently in Camp David "closely watching the path and doings of Hurricane Harvey".
At the request of the Governor of Texas, I have signed the Disaster Proclamation, which unleashes the full force of government help!— Donald J. Trump (@realDonaldTrump) August 26, 2017
He earlier encouraged everyone in the path of the storm "to heed the advice and orders of their local and state officials".
The National Hurricane Centre described the storm as "life-threatening, dangerous and catastrophic".
Mayor of Rockport, Patrick Rios, warned residents remaining in the area to "mark their arm with a Sharpie pen with their name and social security number" to make it easier for rescuers to identify them.
Seven counties in Texas have ordered mandatory evacuations, and tens of thousands of people left their homes ahead of the storm's arrival.
Petrol prices shot up along the south Texas coast as stations ran out of fuel, and there have been reports of inflated consumer prices in some Texan supermarkets.
Mr Trump is expected to visit Texas early next week.