The soldier, Elor Azaria, has been on trial for manslaughter in a military court since May, with right-wing politicians defending him despite top army brass harshly condemning the killing.
He now faces up to 20 years in prison after being convicted for manslaughter.
The shooting in March last year set off intense political debate, with Prime Minister Benjamin Netanyahu calling his father to express his sympathy.
Others on the right have called for him to be pardoned in an extraordinary public rift between politicians and the country's military.
On Wednesday morning, a few dozen protesters gathered outside Israel's military headquarters in Tel Aviv, where the verdict was to be announced, holding a sign that read: "People of Israel do not abandon a soldier in the battlefield".
The case burst into public view when a video of the March 24 shooting emerged and spread widely online.
The video showed Abdul Fatah al-Sharif, 21, lying on the ground, shot along with another man after stabbing and moderately wounding a soldier minutes earlier, according to the army.
Azaria, who was 19 at the time, then shoots him again, in the head, without any apparent provocation.
His lawyers have argued the soldier may have thought the Palestinian was wearing explosives, but he was reportedly already checked for a suicide belt and no one in the video appears to be acting with caution toward him.
Before he became Israeli defence minister in May, Avigdor Lieberman was among those showing strong support for Azaria, including attending one of Azaria's military court appearances in support.
He has since backed away from his earlier stance.
Military chief of staff Gadi Eisenkot has spoken out against the politicisation of the case, warning it could "harm our institutions and our requirements of soldiers".
He said rules on when to open fire must be followed.
"An 18-year-old man who serves in the army is not our child, he is not a baby," Eisenkot said in a speech on Tuesday, referring to a campaign by the soldier's supporters calling him the "child" of all Israelis.
