According to official election results, Aubry won 50.02 percent of the votes to edge out her rival Segolene Royal, who received 49.98 percent of the around 137,000 votes cast by party members.
The results will be announced by the National Council next Wednesday. However, Royal, who lost last year's presidential election to Nicolas Sarkozy, contested the result and demanded a new vote.
Aubry's camp shot down the request, saying "there is no reason" for a re-run.
Aubry, 58, is the daughter of former European Commission president Jacques Delors. She is currently mayor of Lille in northern France and will be the first female leader of the Socialists.
