The suspect is thought to be a 26-year-old of Moroccan origin who had lived in Spain, said sources close to the investigation. He was known to the French authorities after being flagged as a potential jihadist by Spanish intelligence services.
Spanish daily El Pais said he moved to France last year and had visited Syria.
Armed with a Kalashnikov assault rifle, an automatic pistol, nine cartridge clips and a box-cutter, the man opened fire on board the TGV train just after it crossed from Belgium into France yesterday.
"I looked back and saw a guy enter with a Kalashnikov. My friends and I got down and then I said 'Let's get him'," Alek Skarlatos, a 22-year-old member of the National Guard in Oregon, told reporters.
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Spencer Stone, who is reportedly in the US Air Force, was the first to reach the gunman who slashed him in the neck and hand with a box-cutter.
"At that point I showed up and grabbed the gun from him and basically started beating him in the head until he fell unconscious," said Skarlatos, who recently returned from service in Afghanistan.
"As soon as we saw him, we all ran back there. It all happened really fast," said Sadler.
"He didn't say anything. He was just telling us to give back his gun. 'Give me back my gun! Give me back my gun!'
"But we just carried on beating him up and immobilised him and that was it."
Stone was taken to hospital along with another unnamed American passenger, who was hit in the shoulder with a bullet.
Mobile phone footage from inside the train and played on several TV stations shows the suspect, a skinny man wearing white trousers and no shirt, flattened on the floor of the train with his hands and feet tied behind his back.
"I'm just a college student," said Sadler. "I came to see my friends for my first trip to Europe and we stop a terrorist. It's kind of crazy.