The Croatian was most recently in charge of the Turkish Super Lig side Trabzonspor and will be tasked with steering the club out of the Bundesliga relegation zone.
"In Nenad Bjelica, we have been able to attract an experienced coach who has worked successfully in various countries," Union president Dirk Zingler said.
"He has a clear idea of how he wants to lead our team and what type of football they should play; we are entrusting him with the task of leading the team to success again."
The capital club parted ways earlier in the month with coach Urs Fischer following a nine-game losing run in the Bundesliga that had left them in last place.
They have since moved up one place to 17th.
The club are also competing in the Champions League but are bottom of Group C with one point after four matches.
Bjelica's first match in charge will be against Portuguese side Braga in the Champions League on Wednesday, followed by a difficult visit to Bayern Munich in the Bundesliga on December 2nd.
