The Germany international has scored 36 goals and contributed 25 assists in 118 appearances for the Bundesliga club.
He is Chelsea’s second most expensive signing after Kepa Arrizabalaga joined from Athletic Bilbao (£71.6m) in 2018.
“I am very happy and proud to be here. It is a dream come true to play in a big club like Chelsea,” said Havertz.
“He is an exciting, dynamic talent. We are delighted to be able to add his versatility and quality to the squad before the season begins.”
Havertz, 21, is Blues manager Frank Lampard’s seventh signing of the summer.
He follows forward and compatriot Timo Werner, midfielder Hakim Ziyech, and defenders Xavier Mbuyamba, Malang Sarr, Ben Chilwell and Thiago Silva to Stamford Bridge.
Sarr will be loaned out, while Mbuyamba has gone into the Blues’ Under-23 squad.
Having graduated from the Leverkusen academy, Havertz scored 18 goals in 45 appearances last season, including eight in the 11 games after the campaign restarted.