Bonatini played a big part in winning the Championship title in 2017/18, scoring 12 goals, but found himself out of Nuno Espirito Santo's plans shortly after promotion to the Premier League.
He has had loan spells at Nottingham Forest and Vitoria Guimaraes over the past couple of years.
The 26-year-old is the latest Wolves player to make the move to Zurich, joining midfielder Connor Ronan and summer recruit Toti Gomes who was immediately loaned there.
Young striker Renat Dadashov had gone there, too, but injured his anterior cruciate ligament in training.
Grasshoppers were bought earlier this year by a firm owned by Jenny Wang, the wife of Fosun owner Guo Guangchang. Former Wolves board member Sky Sun is club president.