He had been due for release on Thursday, but was allowed to leave prison two days early to attend his brother's wedding.
Azaria was filmed shooting dead a wounded Palestinian man who had stabbed three other Israeli soldiers in March 2016.
Footage that was widely shared online and Azaria was subsequently arrested by the Israeli military police.
Following an eight month trial that divided Israeli society, he was found guilty in January 2017, with prominent politicians including Israeli Prime Minister Benjamin Netanyahu calling for him to be pardoned.