The former England Under-21 international's contract was due to expire at the end of the season and having had a taste of the Premier League, he did not want to give it up.
"I was absolutely gutted to go down with Wolves last year but it's a new era, with a new manager, looking to bring in his own players," Kightly said.
"I just felt when you've been at a club a long time you can go a bit stale. I didn't feel like I was going stale but I didn't want that to happen and I felt like I was ready for a new challenge.
"I'll be criticised from the fans and part of me understands that, but I'd like to think if they put themselves in my shoes and weigh up the options I've had, hopefully they can find it in their hearts to agree with me.
"It was a sad day when I left, but I'm really happy to be here and look forward to having a good career at Stoke.
"I think I showed last year that I'm capable of playing in the Premier League and I just want to keep showing people that."
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