Allison departs the Italian squad three years after joining from Lotus.
Mattia Binotto will take on the role of chief technical officer, having previously been power unit director.
"The Team would like to thank James for his commitment and sacrifice during the time spent together, and wishes him success and serenity for his future endeavors," said Ferrari team principal Maurizio Arrivabene.
Allison commented: "During the years I spent at Ferrari, at two different stages and covering different roles, I could get to know and appreciate the value of the team and of the people, women and men, which are part of it.
“I want to thank them all for the great professional and human experience we shared. I wish everybody a happy future with lots of success."
Allison’s departure comes amid a slightly disappointing campaign for the Scuderia, during which they have yet to register a victory.