The Clarets boss strengthened his backline with the arrival of Middlesbrough stalwart Gibson, who cost a joint club-record fee of £15m.
Having got a deal over the line on Sunday, Dyche is pleased to have given the likes of James Tarkowski, Ben Mee and Kevin Long some much-needed competition for a starting place in what could prove to be a long season.
"We are always trying to increase the competitive demand in the group, and last year we carried three centre halves, which is tricky," he told the club's official website. "The demands of the Premier League are there for all to see and, of course we now have the Europa League and we don't know how far that's going to go.
"Then you have domestic cups, so that has to be looked at. Ben is a very competitive player and he will continually push the players. One of the definite demands of being a footballer is when a new face comes in, particularly a high qualify new face. I think he is high quality and he is up for the challenge of competing for the shirt.
"I spoke to him and he's very straight and very demanding. He's captain-type, and has captained his last club, so he has a really strong mentality and I think he knows he is going to have to earn the right, as everyone does here."
Gibson is Burnley's first signing of the summer, with Manchester City goalkeeper Joe Hart reportedly close behind.