The 26-year-old midfielder joined Liverpool last season from Blackpool, but found himself out of favour with new Anfield manager Brendan Rodgers.
He has signed a four-year deal at the Britannia Stadium.
"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 manager Tony Pulis told the club's website.
"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."
Adam said: "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."
He is the fifth player to join the Potters over summer, joining Maurice Edu, Jamie Ness, Michael Kightly and Geoff Cameron.
