Dyche also confirmed Sam Vokes would be heading in the opposite direction.
"We take great pride in Sam and what he has done for this club," the manager explained as he confirmed the transfer to Stoke.
"As has happened before, players move on. He hasn't played as much as he'd like and I understand that.
"As for Peter, he has a hunger to come here and make a mark.
"We know he's a good character and he still has a desire. The main thing for me is having motivated people."