Mail Sport understands the forward first requested to leave the club last summer and he will fly out from Tokyo in the next 24 hours to join up with his new team-mates.
Colombian international Diaz has been a long-term target for the Bundesliga champions despite them seeing an initial bid worth £58.5m rebuffed. Negotiations resumed in recent days and a second official approach has now been accepted.
Diaz, who arrived at Anfield for an initial £37m fee in January 2022, was dropped for the Reds' squad to play AC Milan in their latest pre-season friendly.