Sgt Elor Azaria was found guilty of manslaughter for shooting dead 21-year-old Abdul Fatah al-Sharif in Hebron, in the occupied West Bank, last March.
Azaria had told a colleague that Sharif, who had stabbed another soldier, “deserved to die”.
Military chiefs condemned his actions, but others praised them.
The offence carries a sentence of up to 20 years, though prosecutors had called for Azaria to be jailed for between three and five years.
Sharif’s family had called for Azaria to be jailed for life.
The court dismissed Azaria’s claim that he thought the victim still presented a threat
Azaria, who was also ordered demoted, sat smiling broadly, embraced by his mother, as the judgment was read out.
The judge said his crime was mitigated by the fact that it was his first conviction, that it had occurred in an active military scene and that there had been no clear orders as to how he was supposed to act.
Dozens of right-wing protesters had gathered outside the Tel Aviv Defence Ministry headquarters, where the military court hearing took place.
Israeli Prime Minister Benjamin Netanyahu had said he would support any decision to pardon Azaria.
The killing received widespread coverage after footage of the incident, filmed on a mobile phone, was shown on Israeli news programmes.
It showed Azaria cocking his gun and firing at the head of Sharif, who was lying apparently incapacitated on the ground after being shot and wounded following the stabbing attack.
The court which convicted Azaria dismissed his claim that he had acted out of fear that Sharif might have been wearing an explosive vest.
The case fuelled debate in Israel over when and how soldiers are entitled to use lethal force against attackers.
The killing occurred amid a wave of attacks by Palestinians that had killed 29 Israelis over the preceding five months.
Following the incident military chiefs and the prime minister came under fire from right-wing sections of society – including members of Mr Netanyahu’s cabinet – for criticising Azaria’s actions.
Mr Netanyahu later telephoned Azaria’s father to offer reassurance.