A former Marine has been convicted of murdering American Sniper author Chris Kyle and another man at a Texas shooting range two years ago.

Jurors rejected defence arguments that he was insane and suffered from psychosis.

The trial of Eddie Ray Routh has drawn intense interest, in part because of the Oscar-nominated blockbuster film based on former Navy SEAL Kyle’s memoir about his four tours in Iraq.

• Movie review: American Sniper is ‘myopic, racist’

Since prosecutors didn’t seek the death penalty in the capital murder case, the 27-year-old Routh receives an automatic life sentence without parole in the deaths of Kyle and Kyle’s friend, Chad Littlefield.

Routh showed no reaction in court, even when family members of Littlefield addressed him.

“We’re so thrilled that we have the verdict that we have tonight,” Littlefield’s mother, Judy Littlefield, said at a news conference outside the courthouse.

Kyle’s widow, Taya Kyle, had left the courtroom earlier in the day and had not returned when the verdict was read.

Bradley Cooper earned an Oscar nomination for his role in American Sniper.

Prosecutors and defence lawyers didn’t immediately comment.

The prosecution painted Routh as a troubled drug user who knew right from wrong, despite any mental illnesses.

While trial testimony and 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.

Kyle and Littlefield had taken Routh to the shooting range at Rough Creek Lodge and Resort on February 2, 2013, after Routh’s mother asked Kyle to help her troubled son.

Family members say Routh suffered from post-traumatic stress disorder from serving in Iraq and in Haiti after the devastating 2010 earthquake.

A forensic psychologist testified for prosecutors that 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”.

Routh was ‘straight-up nuts’

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

Among evidence entered by prosecutors was a recorded phone call between Routh and a reporter from The New Yorker magazine in which Routh said he was annoyed Littlefield wasn’t shooting, but instead seemed to be watching him.

Chris Kyle was responsible for 160 kills during his career in the Navy SEALs. Photo: AAP

“Are you gonna shoot? Are you gonna shoot? It’s a shooting sport. You shoot,” Routh said in the phone call.

“That’s what got me all riled up.”

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

“I had to take care of business. I took care of business, and then I got in the truck and left,” Routh said in the phone call.

A resort employee discovered the bodies of Kyle and Littlefield about 5pm; each had been shot several times.

About 45 minutes later, authorities say Routh pulled up to his sister’s home in Kyle’s truck and told her he had killed two people.

She called police, who later found 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?”

“He told us he’d taken a couple of souls and he had more souls to take,” Lancaster police Lieutenant Michael Smith testified.

Routh later took off and led authorities on a chase before the truck became disabled and he was arrested.

-AAP