Hollande met Sauvage's daughters and lawyers on Friday and announced the pardon on Sunday.
"In the face of an exceptional human situation, the president wanted to make it possible for Sauvage to return to her family as soon as possible," the presidency said in a statement.
The 68-year-old was married for 47 years to Norbert Marot, a violent alcoholic who raped and beat her and her three daughters, also abusing her son, who killed himself.
On 10 September 2012, the day after her son's suicide, Sauvage shot her husband three times in the back with a rifle.
The case has become a cause célèbre in France, with campaigners calling for the definition of self-defence to be expanded to encompass victims of violence who act after the violence has taken place.
The move does not quash Sauvage's 2014 conviction but waives the remainder of her sentence.
She is likely to be freed in April.
"I'm overwhelmed, happy, grateful, relieved," said Eva Darlan, founder of an advocacy group for Sauvage.
The group Osez le Feminisme (Dare To Be Feminist) called for the definition of self-defence to be expanded in cases of "female victims of violence".
The feminist campaign Le Collectif national pour les droits des femmes welcomed the pardon but, saying that 84 per cent of victims of domestic violence do not go to the police, commented that "A lot remains to be done".