French newspaper L'Equipe reported that Aulas was due to remain president for three more years but the new American ownership is looking to make substantial changes to the club's structure.
Aulas will remain honorary president, the club said, adding that Textor will be interim CEO until they find someone new. The decision was taken during a meeting held on Friday.
"OL Groupe sincerely thanks Mr Jean-Michel Aulas for his commitment and unreserved dedication to Olympique Lyonnais over more than three decades, during which time more than 50 titles have been won for both the men's and women's teams," the club said.
"The priority of the new Chairman and CEO and the Board of Directors will be to strengthen Olympique Lyonnais' position on the world football stage, in line with the highest ambitions of its illustrious history."
Lyon are seventh in Ligue 1 with four games remaining.
