Fankhauser will retain his current role of leading Thomas Cook markets including Germany, Belgium, Netherlands, Austria, Switzerland and Russia.
He will work closely with Ian Ailles and Phil Aird-Mash, the chief executives of the UK mainstream and independent businesses respectively.
Both Ailles and Aird-Mash will report to Fankhauser and their positions will remain the same, while Fankhauser will report to Green.
Fankhauser has been tasked with continuing with the "transformation" of the business's performance, simplifying the UK's operating structure, and accelerating its ongoing "turnaround" plan.
Green said: "Transforming the performance of our UK and Ireland business will, in essence, transform the Thomas Cook Group's performance overall.
"Peter has extensive experience and a proven track record of successfully leading and transforming businesses, and I'm confident that by bringing our UK and continental European operations together, we will achieve far greater synergies for the group and significantly improve operational efficiency, the sharing of best practice, and driving out siloed behaviour."
Thomas Cook has already undergone significant managerial and marketing changes, appointing Green as group chief executive in May, following the resignation of Manny Fontenla-Novoa nearly a year earlier.
Last month, the operator confirmed that Mike Hoban, the chief marketing officer at Confused.com, had been appointed as the new director of marketing, brand and customer insight, replacing Michael Johnson, who had led Thomas Cook's new brand work this year.Follow @loullamae_es