He succeeds Silvano Cassano, who stood down in September after less than a year in charge of Italy’s biggest airline.
Mr Ball, appointed chief executive officer of Jet in May 2014, will take over at Alitalia next March, the company said yesterday.
The two carriers are linked by their membership of the seven-strong Equity Alliance developed by Etihad Airways PJSC, which owns 49% of Alitalia and 24% of Jet.
Mr Ball will take forward Mr Cassano’s plan to reposition Alitalia as a more upscale operator, differentiating it from discount rivals as it targets a return to profit by 2017.
The revamp is crucial to Etihad’s efforts to tap European traffic via affiliates that also include Air Berlin and Air Serbia.
“Cramer is the right person to continue leading the development and implementation of our industrial plan, which is now well in motion,” said Alitalia chairman Luca Cordero di Montezemolo.
Mr Ball, an Australian like Etihad CEO James Hogan, has had a 20-year career in aviation.
He previously worked at Ansett Australia, Qantas Airways, Gulf Air of Bahrain, and Etihad itself, before two years running Air Seychelles, in which Etihad has a 40% stake, where he oversaw a return to profit in 2012 and 2013.