The 19-year-old moves to Merseyside with his Blues' contract having expired this summer. A compensation fee for the deal is expected to be decided by independent tribunal.
Chelsea are thought to have been pushing for towards £10 million although Solanke had not played for the club since making his first-team debut in October 2014, with the Reds hoping to pay nearer to £3 million.
Solanke - who recently won the U20 World Cup with England alongside Liverpool youngsters Sheyi Ojo and Ovie Ejaria - will take the No.29 shirt at Anfield.
The teenage forward scored four goals and was named the tournament's best player in South Korea last month, off the back of a disappointing campaign in which he was frozen out of Antonio Conte's senior squad.
Liverpool beat a number of clubs to Solanke's signature with the player himself acknowledging the lure of Reds boss Jürgen Klopp in attracting him to pen a deal on L4.
Solanke netted 41 goals at youth level for Chelsea in 2014-15 as the Stamford Bridge youngsters won the UEFA Youth League and FA Youth Cup and was considered one of the London outfit's best young talents.
He spent the following season on loan at Vitesse Arnhem, scoring seven goals in 25 Eredivisie appearances, but is understood to have become frustrated at a lack of first-team opportunities.
Striker delighted to join Liverpool
Solanke has already been pictured training with Liverpool's senior squad at their Melwood training base, Klopp's charges having reconvened for pre-season training on Wednesday. He could make his uncompetitive debut against Tranmere Rovers this week.
Upon confirming his move, Solanke told Liverpool's official website that it "feels amazing" to have signed and that "everyone" at the club has made him "feel welcome already."
He added: "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."
Having played behind Everton attacker Dominic Calvert-Lewin for his national team last month, Solanke was asked about his best position, to which he responded: "My favourite position would probably be the striker, number nine, but I can play behind the striker as a No.10 or out wide, so I think I’m quite versatile."
Solanke is expected to go straight into Liverpool's under-23s team, headed by Neil Critchley, who has been promoted from being under-18s boss last term.
There, he will compete with the likes of Rhian Brewster and Glen McAuley for a central striking role - while it is likely his first-team chances in the 2017-18 season will come in domestic cup competitions.