The striker, who won the player of the tournament award at the U20 World Cup this summer after helping England to the title, will wear the No 29 shirt at Anfield.
Liverpool’s statement did not specify the length of Solanke’s contract, while Chelsea’s compensation fee will be set by a tribunal.
“It feels amazing and everyone has made me feel welcome already,” the 19-year-old told his new club’s website.
“Even just pulling on the training top, I was over the moon. Hopefully I can put on the shirt in the near future and make some good history here.”
Solanke had been with Chelsea’s academy since 2004 but made just one first-team appearance and spent the 2015.16 season on loan at Vitesse Arnhem.