Elor Azaria entered the Tserifin military base near the city of Rishon LeZion to begin serving his sentence.
He arrived in a car festooned with photographs of him and Israeli flags, while motorcycle-riding supporters accompanied him along the route.
A few dozen supporters waved Israeli flags and chanted Azaria's name as the car pulled up.
On July 30, a military court rejected Azaria's appeal against his conviction for manslaughter and upheld the prison sentence.
It showed Abdul Fatah al-Sharif, 21, lying wounded on the ground, shot along with another Palestinian after stabbing and wounding a soldier, according to the army.
Azaria then shot him in the head without any apparent provocation.
He said he feared Sharif was wearing an explosive belt and could blow himself up, a claim judges rejected.
A number of Israeli leaders, including Prime Minister Benjamin Netanyahu, have spoken out in favour of Azaria being pardoned.
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