"I want to win titles," says Switzerland forward after moving to Anfield on long-term deal
It is understood Stoke accepted a bid of just over £13.5m after Liverpool met the release clause valuation in the Swiss midfielder's contract.
Shaqiri becomes Liverpool's third summer signing after Fabinho and Naby Keita joined the club and he is keen for the Premier League season to get underway.
"I'm very happy to be here. It's a huge club with big history, big players and a fantastic coach. So I'm really glad and happy to be here," Shaqiri told "As a player you always want to be on the biggest stage in football. A few years ago I wanted to come too but it didn't happen. I'm really happy that now I'm finally here.
"I want to improve myself too, I want to be with the best and I want to win titles. That's what I'm here for."
The 26-year-old, who was part of the Switzerland squad which reached the round of 16 at the World Cup in Russia, joined Stoke in 2015 from Inter Milan before going on to make 84 league appearances for the club.
He started his career at Basel before moving to Bayern Munich where he won two Bundesliga titles, two DFB-Pokal cups and the Champions League, with the Bavarians beating Jurgen Klopp's Borussia Dortmund in the final in 2013.
Klopp believes Liverpool are the "perfect" club for his new signing and described the move as a "no-brainer".
He said: "I think the English phrase to explain the decision to sign Xherdan is a 'no-brainer'. When someone like him becomes available in this way you have to react if you are smart - and we have.
"He has speed and ability, has the right amount of arrogance on the football pitch, real bravery to want the ball and influence things. To play for us these are mandatory requirements.
"We are the perfect move for him in this moment as well I think, because he needs to push himself and challenge himself and our environment encourages that.
"From our perspective, he is someone who makes a big difference to the squad and team, because he can fit in so many positions in our system. He gives us greater flexibility in how we can use our current players also. This is cool.
"I know him well from his time in Switzerland and especially Germany - I have been a long-time admirer. But the added bonus now is that he knows the Premier League and what it takes to perform in this uniquely intense environment."
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