His body was found at Rough Creek Lodge range on Saturday with that of another man. A suspect was arrested.
Mr Kyle, 38, wrote the 2012 bestseller American Sniper, about the psychology of a sniper, in which he said that he had killed more than 250 people.
He served four tours of duty in Iraq and was decorated for bravery.
The gunman opened fire at about 15:30 local time (21:30 GMT) then fled in a pick-up truck belonging to one of the victims, local media reported.
Erath County Sheriff Tommy Bryant said the motive for the killings was unclear, and was unable to explain how the two men were shot.