Activating a clause in Shaqiri's contract following the Potters' relegation, Liverpool have picked up the Switzerland international for a fairly cheap £13.5 million.
Done swiftly after World Cup exit
Shaqiri has signed a five-year deal, having cut his holiday short to have a medical on Friday.
Liverpool, Stoke and Shaqiri had all finalised negotiations by the end of last week, but allowed the transfer to be put on hold for a few days as the 26-year-old continued to rest on holiday after competing at the World Cup for Switzerland.
Shaqiri impressed at the World Cup, scoring a winner for Switzerland against Serbia, before they were knocked out at the last 16 stage by Sweden.
That early exit will allow him to join up with Klopp's squad in a couple of weeks, likely in the middle of their US tour, as they gear up towards their season opener at home to West Ham United in four weeks time.
His playmaking abilities also offer the potential for him to play in a deeper role, although his chances there may be lessened should Liverpool complete the potential signing of Nabil Fekir.
Regardless, his signing comes as a boost for Liverpool fans who were often left frustrated at their side turning to the inexperienced Dominic Solanke when things were going wrong in matches last season.
Shaqiri's eight league goals and seven assists in a poor Stoke side last season demonstrated his talents, whilst his set-piece abilities will be welcomed even more after Philippe Coutinho's Anfield departure in January.