The Reds have triggered the release clause in Shaqiri's contract at the Bet365 Stadium, and unless there are complications, the Swiss winger will become Jurgen Klopp's third summer signing in the coming days.
Shaqiri was at Bayern Munich and Inter before joining Stoke in 2015, so it was always unlikely that he would remain a part of Gary Rowett's squad following the Potters' relegation to the Championship in May.
There were reports of interest from across Europe, particularly after some good performances for Switzerland at the World Cup, but the Liverpool Echo reports that it is Liverpool who have snagged the deal.
Shaqiri will get a brief rest after Switzerland's last 16 elimination against Sweden, before joining up with the Liverpool squad for their pre-season tour of America later this month.
The 26-year-old never found consistency for Stoke but Liverpool is the sort of club and Jurgen Klopp the sort of manager who can get the best out of him.
Shaqiri may be a valuable player in the absence of Alex Oxlade-Chamberlain, who is sidelined until November at the earliest, having suffered a knee injury in Liverpool's Champions League win over Roma in April.
He will also provide important backup to Liverpool's wide forwards, Mo Salah and Sadio Mane. The Reds have lacked any depth in this area since the sale of Philippe Coutinho to Barcelona in January.
Shaqiri will join Naby Keita and Fabinho in the new arrivals lounge at Anfield this summer, though it's unclear whether or not Liverpool plan to bring in any defensive reinfocements.