Pisa, who were relegated from Serie A last season, had themselves paid Bologna in the region of €4.5m to sign the 29-year-old, meaning Union are paying a broadly similar fee to bring him to the Bundesliga after his brief spell in Tuscany.
Union's managing director of professional football, Horst Heldt, praised the versatile midfielder on completion of the move.
"Michel is a very intelligent and versatile midfielder who has consistently delivered his performances at a high level for many years," Heldt said.
"He brings international experience, leadership qualities and a high level of tactical discipline. His style of play gives a team balance and stability, while he also has the quality to make his own mark going forward."
Aebischer played a significant role for Switzerland at this summer's World Cup, starting two matches in central midfield for the Swiss national team. Union are expected to use him in the same role, with 1. FC Köln also having registered interest in the player before his move to Berlin.
"Union is a club with a clear identity and special values," Aebischer said. "In conversations with the people in charge, I quickly sensed how much importance is placed on cohesion and team spirit here. After my time in Switzerland and Italy, I'm now looking forward to the Bundesliga and to bringing my experience here.
"I want to take on responsibility on and off the pitch and share a successful time with the team."
The Swiss midfielder made his name at Young Boys Bern before joining Bologna in 2022, where he won the Coppa Italia in 2025, and spent last season on loan at Pisa before the move to the Serie A club was made permanent. He has now made the step up to a top-flight side once again, joining Union under head coach Mauro Lustrinelli.
At Young Boys, Aebischer won four Swiss championships and a Swiss Cup between 2018 and 2021, also gaining experience in the Champions League and Europa League before his switch to Italy. He has earned 44 caps for Switzerland since making his international debut in 2019, and has now featured at a World Cup, a European Championship and a second World Cup across his international career.