
Routh was found guilty of fatally shooting Kyle and Kyle’s friend, Chad Littlefield, multiple times at a gun range about 70 miles (110 km) southwest of Fort Worth in February 2013.
Prosecutors said he ambushed the two from the rear, waiting for Kyle to completely unload his weapon at the range before he attacked with a barrage of gunshots.
Jurors returned the verdict against the former Marine, whose lawyers had mounted an insanity defence and argued he suffered from psychosis.
The 27-year-old was given an automatic life sentence without parole at a court in Stephenville, Texas, for the deaths of the Navy SEAL and his friend Chad Littlefield.
Kyle, a former rancher had turned SEAL credited with the most confirmed kills of any U.S. military sniper, has been lionized in his home state of Texas.
He became entrenched in U.S. popular culture in large part due to his best-selling book and the Academy Award nominated movie directed by Clint Eastwood and starring Bradley Cooper.
After leaving military service, Kyle, who battled his own mental demons, helped counsel troubled veterans with trips for shooting and talks. He had driven Routh to the range with Kyle’s neighbor, Littlefield.
Even though Kyle’s autobiography has been criticised for language seen as demeaning Iraqis and had been on the losing end of a defamation suit brought by former Minnesota Governor Jesse Ventura, Kyle is revered in Stephenville, near where he grew up and went to college.
Defence lawyers said Mr Kyle described Routh as “straight-up nuts” in a text message to his friend as they drove to the shooting range.
They added that the defendant, who had been prescribed anti-psychotic medication used to treat schizophrenia, believed the men were planning to kill him.
A forensics expert said both men were shot in the back at close range and were hit by 12 or 13 bullets.
The trial had drawn huge interest because of the blockbuster Oscar-nominated film based on the former Navy SEAL’s memoir about his four tours in Iraq.
In closing arguments, prosecutor Jane Starnes said Routh acted coldly and deliberately when he gunned down the two and then plotted his escape.
“That is not insanity. That is just cold, calculated capital murder,” Starnes said.