A Texas jury has found Eddie Ray Routh guilty of the murder of US Navy Seal Chris Kyle, who wrote American Sniper, and his friend Chad Littlefield.

The judge sentenced Routh to life in prison without parole; prosecutors had not sought the death penalty.

Defence lawyers for Routh said the 27-year-old was psychotic at the time of the shootings two years ago.

But prosecutors said Routh was aware of what he was doing when he gunned the pair down at a Texas gun range in 2013.

The film based on Kyle's memoir of his four tours of duty in Iraq was nominated for best film at the Oscars this year.

The former Navy Seal, who has the most recorded kills of any US sniper, was shot and killed along with Littlefield at a rural shooting range south-west of Fort Worth.