The 37-year-old has been responsible for finance, human resources and technology at the carrier since the start of the month.
He succeeds Jörg Beissel, who is joining the Lufthansa Group after three years as managing director and chief financial officer at Eurowings.
Bauer said: “The Eurowings Group has put in a massive effort this year, laying down the groundwork for becoming one of Europe’s leading point-to-point airlines in the years to come.
“I am delighted to be part of the Eurowings Group team which has achieved significant growth over the past twelve months with approximately six million additional passengers, 77 additional aircraft and 3,000 new employees.”
An industrial engineer by training, Bauer is married and has two children.