It has not been announced how long Solanke's new contract will run for, while the compensation fee for Chelsea will be set by a tribunal.
The 20-year old, who won the best player award at the U20 European Championships last month, will don the number 29 jersey for his new club.
"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."
#LFC can announce the signing of @DomSolanke: https://t.co/8Ltssjvgpkpic.twitter.com/B1s3gMeSpx
— Liverpool FC (@LFC) July 10, 2017
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