Cerutti, currently president of Christie’s Europe, was poached by the firm last year from Sotheby’s where he was chief executive of its French business and European deputy chairman. He officially joined Christie's in September.
The management shuffle, to take effect in January, will see French owner François Pinault become chairman, a role that Barbizet currently holds alongside being chief executive.
Barbizet had taken the helm in 2014 from American Steven Murphy who left the firm.
She is a close confidant of Pinault and has worked for his companies for more than 20 years.
Pinault said: “Two years ago I asked Patricia to take the helm and adapt the organisation to the new challenges of the art industry and market.”
He said it is now appropriate for her to "pass the baton".
Following these changes, Stephen Brooks will continue as deputy chief executive and Jussi Pylkkänen will continue in his role as global president.
