The Italians, who also own Spanish club Granada and Italian outfit Udinese, took over the Hornets from Laurence Bassini last week and have immediately relieved Dyche from his role at Vicarage Road.
"On behalf of the club, the Pozzo family acknowledges that Sean's positive contribution to Watford FC dates back long before his appointment as manager in June 2011," read a statement on the club's official website.
"The Pozzo family also recognises Sean's impeccable conduct, representing the Hornets with honour and dignity at all times.
"His achievements under difficult circumstances mean that he will rightly be held in high regard by Watford supporters.
"Everyone at the club extends their warmest wishes to Sean for the future."