Gibson joined the 'Clarets' in a £15m move earlier this summer and made his debut in the extra-time victory over Istanbul Basaksehir in the Europa League on Thursday night.
His contribution in keeping a clean sheet is unlikey to earn him a place in the side for the return to league action against Watford on Sunday, with Ben Mee and James Tarkowski set to return to the side.
Nevertheless, Dyche has been impressed with his new recruit's attitude since making the move to Turf Moor.
"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 explained.
"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 [with Boro] 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.
"Ben Gibson, without doubt, is a man, a leader, I can’t smell anything other than that on him."
Meanwhile, Dyche also voiced his admiration for Gibson joining the club with the aim of breaking up that Mee-Tarkowski axis.
"That’s the challenge, and he’s brought into that," he explained.
"He wants to do well for himself, he’s taken a big commitment to come here, and he knows.
“He’s seen it, there’s an honesty to players like him, he’ll be looking (at Mee and Tarkowski) thinking ‘these are decent players’ but, how can you not admire a player who knows he’s coming into that and saying ‘yeah, I want a piece of it. I want to go and challenge.’
“So we’re looking forward to what he can offer when he gets a chance."