The Primera Division champions said the deal for the 17-year-old, who has not made a first-team appearance for the Catalan giants, could reach 12 million euros (£10million).
A Barca statement read: "Tonny Sanabria will join Sassuolo after reaching an agreement for 4.5million euros which could be 12 depending on the performance of the player and his future market value.
"The process to purchase the player started with Roma, but the transfer was closed with Sassuolo."
Sanabria made his debut for Barcelona B this season after joining the club's youth academy in 2010 and has played a total of 10 matches in Spain's Segunda Division for the reserve side, scoring three goals.
He made his international debut for Paraguay during qualification for this summer's World Cup.
Sassuolo are third from bottom in the Serie A standings with 17 points, one adrift of safety after 21 games played.
Earlier on Wednesday they appointed former Genoa manager Alberto Malesani as their new coach.
Malesani takes over from Eusebio Di Francesco, who was sacked on Tuesday after 19 months in charge following the team's poor run of form.