Adam failed to make an impact during his one season at Liverpool and he was deemed surplus to requirements as manager Brendan Rodgers signed Joe Allen and Nuri Sahin.
When asked about his reason for joining Stoke, Adam told BBC Radio Stoke: "It was football, I want to play every week.
"As a footballer you want to play football. When an opportunity like this comes along, it's hard to turn down.
"It's a well-established club in the Premier League and hopefully we can be successful in the next few years."
Adam made his debut in Stoke's 2-2 draw with Wigan Athletic on Saturday.