New owner Giampaolo Pozzo announced on Monday that Zola will manage Watford this season, and has moved a step closer to the appointment by dispensing with Dyche's services.
Dyche had been at Vicarage Road since June 2011 and led the club to 11th in the table last season, their highest finish for five seasons.
Pozzo purchased the Championship club last week and says he has reached a verbal agreement with former Chelsea striker Zola, who was sacked by West Ham in the summer of 2010.
"The Watford deal was conducted by my son [Gino], who works a lot in London," Pozzo told Sky Italia.
"We are trying to revive a historic club and to bring it back to the Premier League. Zola? We are on the right path and hence I believe he will be our new coach. We have a verbal agreement.
"The English coaches are different to that of the Italians in terms of managing. Before deciding on the coach we needed time. My son will be in London as well tomorrow and there should be no problem."