The Clarets held off a number of clubs to secure the signing of Gibson from Middlesbrough, and the Englishman starred as Burnley progressed past Istanbul Basaksehir in the Europa League on Thursday night.
Gibson could find himself back on the bench for the Premier League fixture with Watford, but the left-sided centre-back is already well regarded by his new manager.
Dyche is quoted by Sky Sports News as saying: "I don't know Ben that well yet but he's come in with the right manner. He's a very serious professional and we like that here.
"He looks after himself, he's very fit and he handles himself in the right manner. He's had one season in the Premier League so he's still developing as a player. Games like Thursday will do him no harm at all.
"You want competitive spirit, you want guys to be knocking on the door."
Gibson has penned a four-year contract at Turf Moor.