The Swiss international winger is the Reds' third major purchase of the summer, and has penned a five-year deal at Anfield.
Shaqiri will link up with Jurgen Klopp's squad for their three-game tour of the United States, where they will play in the International Champions Cup against Borussia Dortmund, Manchester City and Manchester United.
The 26-year-old scored eight times in the Premier League for Stoke last season, but was unable to save the Potters from relegation. He helped Switzerland to the last 16 of the World Cup in Russia, where they were beaten by Sweden.
Shaqiri revealed his delight at moving to Anfield, claiming that he was eager to work with Klopp and play for such a big club.
“I’m very happy to be here," he told the club's official website. "It’s a huge club with big history, big players and a fantastic coach. So I’m really glad and happy to be here.
“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.”
Klopp is excited to see what his new addition can add to the club, indicating that it was the right time for Shaqiri to transfer to a team in the Champions League and push himself to the next level.
“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,” Klopp said.
“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. We will want him to express himself but also learn and improve the areas of his game where he can still make progression.
“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."