Eddie Ray Routh was jailed for life without the possibility of parole on 24 February after a Texas jury found him guilty of murdering Chris Kyle, the former US Navy SEAL whose autobiography was turned into the hit movie American Sniper.

Routh, a former US Marine, was found guilty of fatally shooting Kyle and Kyle's friend, Chad Littlefield, multiple times at a gun range about 70 miles south-west of Fort Worth in February 2013.

Kyle, who helped counsel troubled veterans with trips for shooting and talks, had driven Routh to the range with Kyle's neighbour, Littlefield.

Speaking outside the court, Littlefield's mother Judy said she was grateful for the verdict.

"We just want to say that we've waited two years for God to get justice for us on behalf of our son and as always God has proved to be faithful and we're so thrilled that we have the verdict that we had tonight. And thank you guys for being so compassionate and treating us with respect and honouring us," she said, referring to the media.

The jury deliberated for a little more than two hours before reaching a verdict at a court in the rural Texas city of Stephenville. Prosecutors had been seeking a life sentence without parole.

Defence lawyers argued that Routh was a paranoid schizophrenic and should be declared innocent by reason of insanity.

In closing arguments, prosecutor Jane Starnes said Routh acted coldly and deliberately when he waited for Kyle to empty his gun at the range and then ambushed the two from behind before fleeing the scene in Kyle's pickup truck.

The judge told jurors they could find a person innocent by reason of insanity if the defendant did not know the conduct was wrong due to a severe mental defect or illness.

Prosecutors said the two were shot by 12 or 13 bullets and that Routh put on an act to get out of trouble.

Jurors saw police videos where Routh confessed to the killings in a rambling speech and heard audio tape of a prison phone call to a reporter where he talked about shooting Littlefield first, saying he was angry that he came to the range.