The 50-year-old Swiss replaces Marie-Louise Eta, who had taken charge in April on an interim basis following Steffen Baumgart's departure and became the first woman to lead a men's Bundesliga team.
Lustrinelli, a former Switzerland international, took over at Thun in 2022 and led them to the second division championship and promotion in 2025 before winning the Swiss league crown this season.
“Mauro has demonstrated in recent years how he can shape and develop teams. Winning the championship title with a promoted team speaks to his technical quality, but also to his ability to lead and inspire a group,” said Horst Heldt, Union's director of football, in a statement on Thursday.
“We are convinced we have found the right coach for this and look forward to working together.”
Union finished the Bundesliga season in 11th place and missed out on European football next season.