The 27-year-old has signed a five-year contract will wear the No 26 shirt.
Reports in the Liverpool Echo last week claimed that ex-Reds' defender Phil Thompson has urged his former club to sign the Leicester man following his scintillating tournament, and it now remains to be seen whether an advance will be made after the World Cup.
Several positions remain problematic for the Reds and if they are serious about toppling current champions Manchester City next season they must ensure that the right players are added to the squad this summer.
"Watching them from afar has been a pleasure".
Leicester had already brought in cover with the £24m arrival of attacking midfielder James Maddison from Norwich.
The club wished him all the best in his new adventure.
According to the Daily Mail, the Algerian global is set for a medical at Manchester City between Sunday and Tuesday.
"His moments of magic will live long in the memory as the club and its fans continue to build a long-term legacy for the success delivered by the teams to which Riyad so memorably contributed".
Interestingly, the Algerian was back in Leicester's good books as he netted four more goals for the Foxes, taking his total goals to 39 goals from 139 top flight games for the King Power dwellers.