Orban, 24, emerged as one of the finest young central defenders in the Bundesliga in Leipzig's remarkable maiden season. In his 28 top-flight appearances, he frequently took the armband from club captain Dominik Kaiser, who only made seven league starts.
As well as helping his side earn the third-best defensive record behind Bayern Munich and Hoffenheim (39 goals conceded), he chipped in at the other end of the pitch, scoring goals against Bayer Leverkusen, Hertha Berlin and Darmstadt.
"Willi Orban will be the new captain," Hasenhüttl announced on Friday, ahead of Leipzig's season opener against seventh-tier Sportfreunde Dorfmerkingen in the first round of the DFB Cup. "He always sets an example and is well-respected within the team."
Orban joined RBL from Kaiserslautern in the summer of 2015 and quickly established himself as a first-team regular, playing a key role as the club won their first promotion to the German elite under Ralf Rangnick. He will now have an opportunity to showcase his leadership abilities as Leipzig look to build on their fantastic 2016/17 campaign and get a first taste of the UEFA Champions League.
"I'm the kind of guy who is happy to take on responsibility," Orban beamed in Friday's press conference. "It's a real show of faith from the club, and I want to justify their decision. As captain, I want to lead the way with my performances and be a link between the team and the management."
Leipzig kick off their Bundesliga season at Schalke on 19 August, and they will discover their opponents in the Champions League group stage when the draw is made on 24 August.