City boss Tony Pulis said: "He is very fit and strong and he could potentially be our 20-goal-a-season striker."
Carl will be taking a 50% pay cut in his move to the potteries.
"Taking a 50 per cent pay cut will hopefully show people I'm here to play football, not for the money," said Asaba. "For me, it's simply about playing, enjoying my football, working hard and getting results.
"And it's not just about survival, but pushing on. I know Stoke struggled last season, but the team is in transition and the gaffer is still trying to bring in the players he wants.
"Stoke has always struck me as a team capable of playing football and playing it tough. It's a case of getting the right balance between such things as strength and skill, older heads and the young talent coming through the Academy.
"When the gaffer speaks about the club you cannot fail to be impressed. The fans are awesome and the set up fantastic. I'm champing at the bit."