The verdict is the first-ever death sentence passed by a Pakistani court on a serving member of the military, according to lawyers.
Shahid Zafar, a member of the Rangers force which comes under the interior ministry but is considered to be part of the armed forces, was found guilty of pulling the trigger and sentenced to death and a 200,000-rupee (1,600-euro) fine.
Five other Rangers were jailed for life, as was the civilian who accused Shah of robbery and dragged him over to them. They each have to pay 100,000 rupees to the victim’s family.
The widely aired footage of the killing showed a cleanshaven and unarmed Shah pleading for his life before he is shot twice. He then begs for help while the soldiers watch him lose consciousness.
"The decision is historic, it shows no one is above the law," government prosecutor Mohammed Khan Buriro told reporters.
Interior Minister Rehman Malik earlier said that the victim had been carrying an unlicenced weapon but no evidence of the claim was found.
The case focused attention on arbitrary violence by the military in Pakistan.
Rights campaigners point out that they were formed for combat and border duty and are not trained to work in civilian areas.