Chris Kyle shot: Ex-US Navy Seal Sniper Shot Dead
It is believed the 38-year-old had been helping a soldier who was recovering from post-traumatic stress disorder.
Local newspapers have quoted Erath County Sheriff Tommy Bryant who said the pair were found dead on Saturday afternoon at Rough Creek Lodge's shooting range, which is about an hour from Fort Worth.
The Star-Telegram reported that witnesses told police a gunman opened fire on the men, then fled in a truck belonging to one of the victims.
The newspapers said a 25-year-old man was later taken into custody in Lancaster, southeast of Dallas. The motive is unclear.
Scott McEwen, who co-wrote American Sniper, paid tribute to his friend.
"It just comes as a shock and it's staggering to think that after all Chris has been through, that this is how he meets his end, because there are so many ways he could have been killed," he said.
American Sniper: The Autobiography of the Most Lethal Sniper in US Military History details Kyle's four combat tours of duty in Operation Iraqi Freedom and the two Silver Stars and five Bronze Stars he was awarded for bravery.
It has been claimed he killed 160 people during his career.
After leaving the Navy he founded Craft International, a company that provided combat and weapons training to military, police and corporate and civilian clients.