The financial details of the deal have not been made public, but it is reported that Milan paid around 34 million euros, plus an additional three million euros in bonuses, for the 23-year-old player.
Jashari has previously played for Luzern in Switzerland and made 52 appearances for Club Brugge in all competitions, scoring four goals. He has also played four times for the Swiss national team.
Before joining Milan, Jashari helped Club Brugge reach the Champions League last 16 this year. Milan's Serie A season is set to begin on August 23, with a home match against promoted team Cremonese.