The German giants in April disclosed that Jerome would be leaving after 10 years at the club.
Struggling to find himself a starting berth at Bayern, the defender has finally moved to Lyon.
Boateng in his stay at Bayern won 22 trophies including the Champions League twice and the Bundesliga nine times.
The 32-year-old also won five German Cups, two Club World Cups, two Uefa Super Cups and two German Super Cups with Bayern.
Boateng who is Lyon's fifth summer signing attracted interest from a number of Premier League clubs over the summer, including Chelsea, Arsenal and Tottenham.
With Jerome failing to extend his stay at the Allianz Arena, Bayern sporting director Hasan Salihamidzic said it had been a "joint decision" which involved the club's management team and that Boateng had been "very understanding".
Jerome Boateng signed for Bayern in 2011 from Manchester City and is one of their most decorated players of all time.
Jerome, regarded as one of the big names in football follows the footsteps of Argentine wizard Lionel Messi and experienced Sergio Ramos who all have joined Paris Saint-Germain from Barcelona and Real Madrid respectively.
Jerome is expected to make his debut for Lyon when the league resumes after international break.
Lyon have won just one of their four league games thus far and will host Strasbourg in their next fixture.
