The storm reached landfall at 17:00CT (23:00BST) according to the US National Hurricane Centre.
First to be struck was Padre Island, situated off the coast of southern Texas.
Hanna’s speed makes it a high-end Category One hurricane by US definition.
In response to the hurricane Texas governor Greg Abbott announced disaster declarations earlier on Saturday for 32 counties.
This means the federal government is allowed to provide “public assistance, direct financial assistance and hazard mitigation assistance”.
The National Weather Service office reported significant structural damage in Port Mansfield, Willacy County.
A hurricane warning is currently in force stretching from Port Mansfield to Mesquite Bay.
In addition a storm surge warning is in place for Port Mansfield to Sargent, meaning life-threatening water surges are possible.
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Hanna has hit Texas before the traditional hurricane season which usually begins a couple of weeks into August.
No other hurricane has struck the state in July since Hurricane Dolly in 2008.
Governor Abbott warned people sheltering together from the hurricane could be vulnerable to coronavirus infection.
He said: “That coming together will continue to provide the ability for Covid-19 to transmit from one person to another.
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“We cannot allow this hurricane to lead to a more catastrophically deadly event by stoking additional spread of Covid-19 that could lead to fatalities.”
The US has seen more coronavirus cases and deaths than any other country in the world.
Separately Hurricane Douglas is currently heading towards Hawaii but is expected to lose its hurricane status before hitting land.