The member for Hollinwood replaces Jim McMahon who won the Oldham West and Royton by-election last month.
Cllr Stretton, who has served as deputy leader since 2014, was chosen over Cllr Arooj Shah, who represents St Mary's ward.
She was elected in 2010 and is chair of the health and well being committee.
Oldham Council will be led by a woman for the first time in its history, after Jean Stretton was selected by Labour councillors.