The 19-year-old joined the Serie A champions from Paris Saint-Germain in 2014 but failed to become a regular in the first team.
He has now opted to join the Bundesliga champions, initially on a two year lona deal but Bayern reserve the option to buy him at the end of the 2016-17 campaign.
The France Under 21 international had his medical on Sunday to complete the move and spoke of his delight to join Pep Guardiola's side.
