Marlon initially joined Barça on loan from Brazilian club Fluminense in 2016, a deal that was made permanent for €5m after an impressive campaign largely spent with the club's B team.
He joined Nice last summer on what was supposed to be a two-year loan with a €20m purchase option, but has now moved to Italy after the deal in France was cut short.
Barça will receive an initial €6m fee and hold both a buy back clause and 50% of the economic rights on any future sale. However, they will forfeit the economic rights on the future sale and instead receive a second payment of €6m if Marlon plays 50 games for Sassuolo.
The 22-year-old is the second centre-back to leave Camp Nou this summer following the recent €31.75m departure of towering Colombian international Yerry Mina to Everton.
Barça bought Clement Lenglet from Sevilla for €35m last month to provide competition for existing options Gerard Pique, Samuel Umtiti and Thomas Vermaelen.