Wawra (pictured), who has been in the post for almost four years, has a contract that expires on June 30, but said he is leaving to "start a new professional project."
"I decided with a heavy heart - but still with full conviction - not to extend my contract," Wawra said in a statement on the club's website. "I loved working here and contributing my part to the big picture.
"As a Sporting Director who is far from finished, I want to develop further in a top environment and get the support of a German Bundesliga club."
Blau-Weiss have started the search for his successor.
The 43-year-old has been linked with SKN St. Polten, and while he has not specifically announced his next destination.
St. Polten, level at the top of the league with Blau-Weiss. have had a partnership with VfL Wolfsburg since 2021.
Christoph Peschek, Managing Director of Blau-Weiss, said: "In the last few weeks I have got to know and appreciate Tino both personally and professionally, which is why we expressed our appreciation of the club with a top offer, taking into account the current situation of the club.
"We tried to convince Tino of an extension with FC Blau-Weiss Linz's great prospects for development. We regret this decision, and Tino was the first to contact me and was instrumental in my starting the engagement in Linz, but his decision is of course acceptable for personal reasons."
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