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.
Kroenke and his son and director Josh put out a joint statement on Tuesday saying that they remain "100% committed to Arsenal" and were not interested in selling a stake in the club despite furious backlash from the fans.
"I want to establish trust with fans and I want to engage the fans again," Ek told business channel CNBC.
The ESL proposal collapsed on Wednesday as founding clubs withdrew one by one following a barrage of criticism from fans, governing bodies and even government officials who threatened to pass legislation to stop the league.
"They appreciate that very well and the people can read and can divide things from one another. The fans expressed their opinion, they were absolutely not happy.