The 26-year-old has signed a four-year contract and joins the Potters for a fee of £4million.
Adam told the club's website: "I'm delighted to be here and to be given the opportunity to work with the club, the manager (Tony Pulis) and the players.
"This club's on the up and it's great to be a part of it. I hope I can help them to improve upon the success which has been achieved over the past few years.
"Hopefully, we can have a successful time together. I can do this club proud and I'm looking forward to the chance of playing in front of their passionate supporters."
Adam is delighted to have joined Stoke and is hoping to get regular first-team football at the club.
"The opportunity to play was getting less and I felt that at my age, I wanted to play every week and hopefully I'll get a chance to here," Adam said.
"It's a great club that is going in the right direction - the foundations are here."
"It's no secret that we've been looking to bring more goals to the squad and Charlie is a fantastic signing in that respect," Stoke boss Tony Pulis said.
"Not only will his creativity and his eye for delivering a pass be a great asset to us, he scored 12 goals for Blackpool in the Premier League two seasons ago.
"We are looking for more goals from all areas of the team and his arrival gives us more competition for places in that department."