The 51-year-old becomes the first German to lead the Austria national side and takes over from Marcel Koller, who is stepping down after six years in the role following the country's failure to qualify for next year's World Cup.
"He knows Austrian soccer well as a player and as a coach," federation president Leo Windtner said. "He is a meticulous worker and can build on the excellent work Koller has done."
Since beginning his coaching career in 2001, Foda has mostly worked with Austrian top-flight side Sturm Graz, where he is expected to remain in post until January.
Foda will lead the team in a friendly against Uruguay next month before preparing for Austria's Euro 2020 qualification campaign.