Solanke made the switch to Merseyside last May after running down his contract at Stamford Bridge.
However, given he was under 24, Chelsea were entitled to compensation having developed him since the age of seven.
Liverpool had initially hoped to pay as little as £3 million for the then-20-year-old, but Chelsea argued his exploits with the England Under-20 side, whom he helped to World Cup glory last year, and his status as a first-team option with the Reds, had increased his value.
The Londoners had hoped to receive more than £10m, with the fee expected to be decided by the Professional Football Compensation Committee.
However, talks between the two clubs have seen the issue resolved directly, removing the need for a tribunal.
Neither club, however, is willing to confirm the exact fee paid. Solanke made 27 appearances for Liverpool last season, scoring his one and only goal on the final day of the Premier League campaign against Brighton.
He was a surprise call-up to the senior England squad too, winning his first cap for Gareth Southgate’s side in a friendly game against Brazil in November 2017.
The Reading-born frontman has been linked with a move away from Liverpool this summer, with Rangers and a host of Premier League clubs keen to sign him on loan.
He will, however, return to Melwood for pre-season training next week, and will be given the chance by Jurgen Klopp to prove himself during the Reds’ friendly fixtures, which begin at Chester a week on Saturday.