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.
United fans protesting against the club's American owners, the Glazer family, stormed into the stadium which was closed to fans due to COVID-19 restrictions.
Greater Manchester Police (GMP) said two officers were injured with one requiring hospital treatment after he was attacked with a bottle and suffered slash wound to his face.