Former US Navy SEAL and best-selling author of American Sniper, Chris Kyle has been shot dead along with another man on a gun range, police in Texas said.

Newspaper reports confirmed that Kyle, hailed as the deadliest military sniper in US history, and a second man were found dead on Saturday at Rough Creek Lodge's shooting range.

Eye witnesses told sheriff's investigators that a gunman opened fire on the men and fled in a pick-up truck belonging to Kyle.

Eddie Ray Routh, an Iraqi war veteran, was arrested hours later after a police car chase led authorities to Lancaster, Texas where Routh was taken into custody on Saturday evening.

Routh, 25, was arraigned on Saturday evening on two counts of murder. The motive for the killings was unclear.

Investigators told ABC affiliate WFAA-TV that Routh is a former Marine who was suffering from post-traumatic stress syndrome.

The name of the second victim has not yet been officially released, but reports indicate he may have been Routh's neighbour.

American Sniper: The Autobiography of the Most Lethal Sniper in US Military History is an account of Kyle's four combat tours of duty in Operation Iraqi Freedom. He was awarded two Silver Stars and five Bronze Stars for bravery.

It has been claimed he killed 160 people during his career. During his tours of duty in Iraq, he was given the nickname 'The Devil of Ramadi'.

Co-author Scott McEwen said he was "staggered" to hear of Kyle's death.

He said: "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."

After leaving the Navy, Kyle founded Craft International, a company that provided combat and weapons training to military, police and corporate and civilian clients.

Ironically, Kyle helped start a charity, FITCO Cares, that works with returning soldiers to help them cope with PTSD - the same ailment that his alleged killer is said to have suffered from.