Zander, 52, was chief designer at Sauber in 2006 and 2007 when they were owned by BMW and will start work with the Swiss-based team in early 2017.
The German also has previous experience with the now-defunct Toyota, BAR-Honda, Honda and Brawn Formula One teams as well as Williams.
"This is a very important step for the implementation of our strategic goals, in order to guide the team into a new and successful era," team principal Monisha Kaltenborn said.
Struggling Sauber have yet to score a point this season and are last in the championship with two races remaining.
The team announced a change of ownership in July, with founder Peter Sauber retiring and handing over control to the Swiss investment firm Longbow Finance.
Audi announced last month that it was leaving endurance racing to focus on the electric Formula E series.
(Reporting by Alan Baldwin in London, editing by Ed Osmond)
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