The troops left Tuesday from their post, which is about 200 miles northwest of Houston, in a series of convoys, a base spokesman said.
The units involved from Fort Hood's 13th Expeditionary Sustainment Command include the 36th Engineer Brigade, 48th Chemical Brigade, 85th Civil Affairs Brigade, 89th Military Police Brigade, 504th Military Intelligence Brigade, 11th Signal Brigade and 1st Medical Brigade.
The vehicles include Humvees, fuel tankers, flat-bed trucks hauling all-terrain forklifts, and Medium Tactical Vehicles.
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Hood has been designated a Federal Emergency Management Agency Incident Support Base for the duration of the crisis.
"Fort Hood stands ready to support state and federal agencies that are aiding our fellow citizens," Maj. Gen. John Uberti, III Corps deputy commanding general, said in a statement. "Our soldiers, who volunteered to serve our nation, are willing and ready to assist as needed."
The convoys to Houston are part of a rapidly expanding National Guard and active-duty military response to the devastation left by Hurricane Harvey and its aftermath of torrential rains and flooding.
On Wednesday, the remnants of the storm made landfall for the third time near Port Arthur, Texas, on a path expected to take it through southwest Louisiana and into Tennessee.
Up to 30,000 National Guard troops, mostly from neighboring states, are on standby to provide assistance in Texas and Louisiana, and the Pentagon has pre-positioned active-duty forces and equipment to respond at the request of Texas Gov. Gregg Abbott and Louisiana Gov. John Bel Edwards.
Marines and their amphibious vehicles are already assisting rescue efforts of firefighters in Galveston, Texas.
-- Editor's note: This story and headline have been updated to correct the name of the command. The troops who deployed from Fort Hood to aid in hurricane recovery efforts in Houston are part of the 13th Expeditionary Sustainment Command, not the 1st Cavalry Division.
-- Richard Sisk can be reached at Richard.Sisk@Military.com.