Haenni has decades of experience following her playing career, having held various posts in women's football at global governing body FIFA for more than a decade.
She was also in charge of women's football at the Swiss football association and sports director at the National Women's Soccer League (NWSL) in the United States among others until her departure earlier this year.
"In our discussions, she impressed us and the committees with her expertise, as well as her combination of specialist knowledge, leadership strength and strategic thinking," said Oliver Mintzlaff, chair of RB Leipzig's supervisory board in a club statement.
The 59-year-old will take up her role on January 1, 2026.
Leipzig, owned by energy drinks maker Red Bull, are currently in second place in the Bundesliga, eight points behind leaders Bayern Munich. The Bundesliga will go into a winter break between December 21 and January 9.
"I am very much looking forward to this new role. I am convinced that with strong teamwork and a focus on RB Leipzig’s strengths, we can tap into significant potential," Haenni said.
"I can’t wait to get started in January and to get to know the club on a deeper level," Haenni said. "Together, we want to continue on what is already a successful path, and achieve our ambitious goals."