The fee for the 19-year-old will be decided by a tribunal, with Liverpool expected to pay around £3m.
Solanke, who is currently part of England's squad at the under-20 World Cup in South Korea, spent the 2015-16 season on loan at Vitesse Arnhem, scoring seven goals in 25 games.
He made one senior Chelsea appearance.
As Solanke is older than 17 and will sign a professional contract, Liverpool's transfer embargo, which is enforced on signing academy players from other England clubs for two years, will not apply.
Celtic were also understood to be interested in Solanke, whose only Chelsea game came as a substitute in a Champions League victory against NK Maribor in October 2014.
Solanke will officially become a Liverpool player on 1 July.
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Liverpool are to sign Chelsea's teenage forward Dominic Solanke after he failed to agree a contract with the Premier League champions.