The 59-year-old Swiss will take over on January 1 and will head Leipzig's management board.
A former footballer, Haenni made 23 appearances for the Swiss national team. Since retiring, she has taken up sports administration roles at UEFA, FIFA and the Swiss Football Association (SFV).
"I can't wait to get started in January and to get to know the club on a deeper level," Haenni said in a statement released Wednesday.
"Together, we want to continue on what is already a successful path, and achieve our ambitious goals."
Former CEO and current Red Bull executive Oliver Mintzlaff praised Haenni's "specialist knowledge, leadership and strategic thinking", adding she would "successfully shape the club’s next stages of development".
Founded in 2009 by taking over a club in Germany's fifth tier, RB Leipzig rose through the ranks and was first promoted to the top flight in 2016.
Since then, the club have won two German Cups and made it to the semi-finals of the Champions League in 2020.
Former Liverpool manager Jurgen Klopp took over as Red Bull global head of football in January 2025, overseeing a multi-club network which includes clubs in Leipzig, New York and Bragantino.