Brigadier John Ridge, who has been coordinating the task force across the Caribbean, said he was “tremendously proud” of British-led relief efforts.
More than 1,100 British troops are deployed in an operation stretching 1,000 miles from Barbados via Anguilla to Turks and Caicos.
Most of the troops on Grand Turk are based at the island’s airport, sleeping on mats often inside mosquito nets, with no running water or electricity.
Brigadier Ridge said: “The way they have just got stuck in has been extraordinary.
“I think it is incredible to go and see young soldiers, young Marines, young sailors, young airmen, interacting and doing amazing stuff and not because they’re told to, because they want to.
“That gives me tremendous pride. For them it has been a hugely rewarding experience.”
He said the damage “varies tremendously” across the territories.
Janice Moore, 53 and originally from Leeds, said: “It really was like the cavalry were coming in when we saw them arrive. They’re brilliant, they’re a massive tonic, a massive boost.”
Lance Corporal Adam Wellstead, of the Royal Engineers, said: “The locals have been really supportive about what we are doing, making us food with what little they’ve got.”