The highly-rated Blues youngster failed to agree terms over a new contract with the Premier League champions, reportedly due to his lack of playing time at Stamford Bridge.
The Reds have reportedly beaten several Premier League clubs, Celtic and RB Leipzig to Solanke's signature, the Englishman moving to Merseyside upon the expiry of his Chelsea contract in July.
A fee for the transfer will be decided by tribunal, with the London side due compensation for the player's development, though reports have suggested Liverpool could have to pay around £3 million.
Liverpool's transfer ban on Academy players from other English league clubs does not apply because Solanke is over the age of 17 and able to sign a professional deal.
Solanke, though he will go into the Reds' under-23s squad, becomes the Reds' first summer signing as Jürgen Klopp looks to bolster his options ahead of a European campaign.
Solanke to initially enter Reds' U23 side
The player is now the German manager's fifth option up top with Roberto Firmino, Daniel Sturridge, Divock Origi and Danny Ings - though some of those players have uncertain futures ahead of the summer.
Early suggestions are that Solanke will earn wages lower than £20,000-a-week because of the club's young player policy.
The teenager has played across all youth groups - U16 to U21 - for England, scoring 23 goals in 48 appearances in total. He was a member of the U17 squad that won the UEFA European U-17 Championship in 2014.
Solanke is currently representing the Young Lions' U20s side in South Korea at the U20 World Cup. He scored a last-minute penalty in their first group game, even captaining them in their final group game, as Paul Simpson's side finished top of Group A to book a last 16 clash with Costa Rica on Wednesday.
The forward, Chelsea's Academy Player of the Year in 2014-15 as he won the FA Youth Cup and UEFA Youth League, ending the season on 41 goals in all competitions after a hat-trick on the final day against Liverpool U21s.
He made his Chelsea debut at 17 as a substitute in a Champions League clash against NK Maribor in October 2014 but has never appeared for their first-team since, spending last season with Vitesse Arnhem in the Eredivisie. Solanke netted seven times in 26 games.
The Blues had offered him a contract extension to the initial three-year deal he signed in September 2014, his first professional deal, but Solanke turned it down to end a 13-year association with the Blues.
He was on the bench for their EFL Cup clash with Bristol Rovers earlier this term but was an unused substitute.