The town of Sassuolo, with a population of just over 40,000, is the smallest ever to be represented in Serie A.
Sassuolo, who climbed from the fourth tier of Italian football to Serie A in 10 years, are one of only four top flight clubs to own their own stadium - although it is 26 kilometres away in the town of Reggio Emilia.
Bucchi was previously in charge of second-tier club Perugia and left by mutual agreement after one season. Before that, he coached Gubbio, Torres and Maceratese in the third tier.
"Thankful for the job done and the results achieved last season, the club wishes coach Bucchi the best of luck in continuing his career," the Serie B club said in a statement (www.acperugiacalcio.com)
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Di Francesco led Sassuolo to promotion to Serie A in the 2012-13 season as they reached the top flight for the first time.
He was fired after only six months of the 2013-14 season but re-hired five weeks later after replacement Alberto Malesani was also dismissed.
He later led them into Europe for the first time as they qualified for the Europa League. Last season, the team were plagued by injuries as they finished 12th.
Sassuolo are the fourth team to have changed coach since the end of last season alongside Inter Milan, AS Roma and Fiorentina.
(Reporting by Silvia Recchimuzzi in Gdynia and Brian Homewood, editing by Ed Osmond and Toby Davis)
