The change at the top of the company came as Cook released annual financial results.
Green, who joined the company two years ago and rescued it from possible collapse, said: “The transformation of Thomas Cook into a company with a market capitalisation of just under £2 billion and a share price of over 130 pence is one I have been proud to lead.
“I always said that I would move on to another company with fresh challenges once my work was complete. That time is now.
“I wish all of the team at this re-energised company continued success, as they move to the next phase of the company’s development.”
Green joined when Cook’s share price was just 14 pence and it had a market capitalisation of £148 million.
Her remit was to transform the company, placing it on a sound financial footing with a solid operational team able to compete in the consumer travel market.
Fankhauser has held a number of senior roles over the last 13 years at Cook.
He will be supported by Michael Healy, who will continue as group chief financial officer, and chief air travel officer Christoph Debus.
Fankhauser said: “I feel very honoured to be leading this business which means so much, to so many people.
“I am determined to work with all our great colleagues worldwide to build on Harriet’s achievements, continuing to deliver great holidays for consumers and good returns for investors.”
Cook chairman Frank Meysman said: “Harriet has had a highly positive impact on this company.
“We emerge from her transformation stronger, with a clear strategy, world-class leadership team, updated brand, and a renewed focus on the customer.
“The succession plan she devised will now take effect and the new chief executive, Peter, will drive the company forward as we focus on winning the commercial battle against other operators.
“Peter is one of the most accomplished and experienced executives in the travel industry and has played a critical role in our transformation to date. We are delighted that someone of Peter’s stature will succeed Harriet and lead the next phase of our transformation”
Sourced from Travel Weekly