The 26-year-old arrives at Anfield for a reported cut-price £13.75 million fee due to a release clause in his contract after Stoke's relegation from the Premier League to the Championship last season.
Shaqiri, who Liverpool previously attempted to sign from Bayern Munich in 2014, joins on a five-year deal and will head to the Reds' pre-season tour in the United States with the rest of the squad next Saturday.
The winger recently returned from Russia, where he scored one and assisted another in four games for Switzerland at the World Cup. He was Stoke City's top goals and assists getter, with eight and seven respectively.
He will wear the No.23 shirt at Anfield, recently vacated by Emre Can who made official his move to Juventus earlier this summer.
“I'm very happy to be here,” Shaqiri told Liverpoolfc.com. “It's a huge club with big history, big players and a fantastic coach.
“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.
“I just want to say I'm really happy to be here. I can't wait to see the fans. I hope we can have a lot of beautiful moments in the coming years.”
Shaqiri is the third signing of the summer so far, joining midfielders Naby Keita and Fabinho. Meanwhile, Liverpool are also thought to be working on a deal for Roma goalkeeper Alisson and could yet go back in for Lyon attacker Nabil Fekir.