Owner Roman Abramovich put Chelsea on the market in early March, just days before he was sanctioned by the British government following Russia's invasion of Ukraine
Frenchman Konate, 22, will join the Anfield club on July 1 once his work permit application is approved and medicals are completed.
Financial details of the transfer were not revealed but British media reported Liverpool triggered a 41 million euros ($49.82 million) release clause in his contract. Konate had a contract until June 2023 with Leipzig.