The 21-year-old, who could cost the Blues a further £18m (€20m/$24m) in team performance-related installments, will take the club’s spending to over £200m ($262m) this summer.
Frank Lampard’s latest signing will mark a new club-record, surpassing the £71.6m (€80m/$95m) paid for Kepa Arrizabalaga in 2018.
The Blues have already agreed on a five-year contract for the attacking midfielder, who met up with his Germany team-mates on Monday in Stuttgart for international duty.
Leverkusen manager Peter Bosz has confirmed he and Kevin Volland, who is expected to join Monaco, is not expected to train with the BayArena outfit again.
“Unfortunately, our squad has not yet been determined,” he told reporters on Monday.
Leverkusen have already lined up their Havertz replacement by agreeing on a €28m (£25m/$33m) fee for Roma forward Patrick Schick.