Miles Evans, 24, showed little emotion as the jury at Bristol Crown Court delivered a majority verdict after more than 16 hours of deliberation.
Choking back tears, Evans appeared at a press conference following Zoe's disappearance in January last year, and promised that the nine-year-old would not be in trouble if she came home. She would be given "lots of cuddles and hugs" and there would be a puppy waiting for her as an early birthday present.
Zoe disappeared from her home in Army married quarters in Warminster, Wiltshire, on 11 January last year, sparking the country's biggest-ever search for a missing child.
Her body was found six weeks later, concealed deep in the undergrowth on Battlesbury Hill, less than a mile from her home. The search cost pounds 1m and involved a total of 150 police, 250 military personnel and scores of members of the public.
Passing sentence, Mr Justice Eady said: "We shall probably never know exactly what happened that night. It is clear from what remained of her body that Zoe was brutalised before her death and must have undergone a terrible ordeal during the last minutes."
As Evans, a private in the Royal Logistics Corps, was led from the courtroom, Zoe's mother, Paula Hamilton, 29, and her grandmother, Ann Hamilton, could be heard weeping from the public gallery.
After the hearing Ms Hamilton said she had no doubt that he would be convicted.
"Only he knows the suffering he has caused and may it remain with him and burden him for the rest of his life," she said in a statement.
Alun Jenkins QC, for the defence, said there would be an appeal.
The court heard that Evans took Zoe from the family home at night and attacked and murdered her outside, possibly after trying to abuse her sexually. He then buried her naked body in an animal hole.
Nigel Pascoe QC, prosecuting, said she died from asphyxiation because her top, a T-shirt with the logo No Fear, was pushed into her mouth as a gag and she inhaled blood from her nose, which had been broken by a blow from Evans's fist.
On the morning of her disappearance, Evans reported for duty as usual at the mechanical transport section at Warminster Barracks.
Laughing and joking, he played computer games with a woman lance corporal, but although considered an able player he lost every game that morning.
When his wife phoned later to say that Zoe was missing, Evans was the dutiful, concerned parent, joining searches for the youngster. That night he went to bed early, saying he wanted to be up early the next day to take part in the renewed search. Two days later, police found Evans's T-shirt in a copse near the rear door of his home and a pair of Zoe's knickers in a nearby field. Both were stained with her blood.
Evans and Ms Hamilton were arrested, but after three days of questioning they were released without charge. Ms Hamilton, who had married Evans only five months before, began to suspect her husband and moved away from the marital home. He was arrested and charged with murder a few days later.
His halting performance at the press conference where he refused to meet the eye of reporters and detectives, had led police directly to him.
He was not the first to have thought he could fool detectives and the media call is becoming an increasingly common weapon for police trying to break down a murder suspect.
Following yesterday's hearing, an Army spokesman said an application for Evans's discharge from the Army would be made in accordance with the Queen's regulations.Reuse content