The 23-year-old attacking midfielder, who has been capped 46 times by Switzerland, has signed for a fee of £12million from Internazionale.
Having agreed a five-year contract, he was unveiled to the media on Thursday ahead of Saturday’s trip to Tottenham.
“I am very happy to be here,” said the former Bayern Munich man. “(Stoke boss) Mark Hughes was very important to me. We have been talking a lot together, and with my brother, with my family.
“For me, it was a perfect decision to come here and it was a big dream always to play in the Premier League.
“For me the Premier League is the best championship in the world.
“I am really happy to be and I can’t wait to get on the pitch, to do what I love and to help this club have a good season.
“We have a good team and I think we can do some good things this season.
“Most important is to integrate fast in this team. I trained today and I feel really good. I am fit and I am excited to be here, I can’t wait to play.”
Hughes thinks the signing of Shaqiri shows how determined Stoke are to improve.
“We are delighted, obviously,” said the manager.
“We are trying to progress as a club and a team, and the only way you can do that is by bringing in top quality players, which Xherdan undoubtedly is.
“We are absolutely delighted to have been able to conclude the deal. It is a big amount of money but we think it will be value, long term.
“We now have a host of top quality players in our squad, to change games and create something out of nothing.”