The 26-year-old has finalised a reported £5m move to the Britannia Stadium, with the Scotland international penning a four-year deal with the Potters.
Adam scored just twice in 37 appearances for the Reds after moving to Anfield last summer, and the midfielder is aiming to score more frequently for his new 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 told Stoke’s website.
“It’s a great club that is going in the right direction – the foundations are here.
“They’ve been progressing ever since they’ve been in the Premier League and it’s great to be part of it and hopefully we can have a successful time together.”
He added: “I want to get back to scoring goals – that was one of the things I didn’t really do last year.
“I’m hoping I can back to that and help the team improve on what they’ve done in the previous four of five seasons here.”
The former Rangers midfielder also revealed he is looking forward to experiencing the vociferous Britannia Stadium crowd as a Stoke player.
“I know they’re a passionate bunch of supporters – every time I’ve been to the Britannia it’s been good and I’m looking forward to being part of it,” he added.
“I’m delighted to be here and to be given the opportunity to work with the club, the manager and the players. It’s a club on the up.”
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