A former US Marine has been found guilty of murdering American Sniper author Chris Kyle and his friend at a shooting range.

Jurors in Stephenville, Texas, returned the verdict against Eddie Ray Routh, rejecting an insanity defence by his lawyers who said he suffered from psychosis.

Since prosecutors did not seek the death penalty in the capital murder case, Routh, 27, receives an automatic life sentence without parole over the deaths of the famed US Navy Seal and his friend Chad Littlefield.

The men had taken Routh shooting at Rough Creek Lodge and Resort in February 2013 after Routh's mother asked Mr Kyle to help him. Family members say Routh suffered from post-traumatic stress disorder after serving in Iraq and Haiti.

The case drew intense interest, largely because of the blockbuster film based on Mr Kyle's memoir about his four Iraq tours.

The prosecution painted Routh as a troubled drug user who knew right from wrong, despite any mental illnesses. While trial evidence often included Routh making odd statements and referring to insanity, he also confessed several times, apologised for the crimes and tried to evade police.

Criminal law experts said the verdict hinged on whether the defence could prove Routh was insane and did not know the killings were wrong at the time they were committed.

Jurors had three options: find Routh guilty of capital murder; find him not guilty; or find him not guilty by reason of insanity. If found not guilty by reason of insanity, the court could have initiated proceedings to have him committed to a state mental hospital.

A forensic psychologist for the prosecution told the court Routh was not legally insane and suggested he may have got some of his ideas from television. Dr Randall Price said Routh had a paranoid disorder made worse by his use of alcohol and marijuana, calling his condition "cannabis-induced psychosis".

Defence lawyers noted Mr Kyle had described Routh as "straight-up nuts" in a text message to Mr Littlefield as they drove to the luxury resort.

The defence said Routh, who had been prescribed anti-psychotic medication often used for schizophrenia, believed the men planned to kill him.

A resort employee discovered the bodies of Mr Kyle and Mr Littlefield, each shot several times. About 45 minutes later, authorities say Routh pulled up at his sister's home in Mr Kyle's truck and told her he had killed two people.

She called police, who later located Routh sitting in front of his home in the truck. A police video shown by prosecutors showed officers trying to coax him from the truck while he makes comments including: "I don't know if I'm going insane" and "Is this about hell walking on earth right now?"