Chelsea appoint Bompastor as new head coach to replace Hayes
The 43-year-old succeeds Emma Hayes, who led the Blues to 14 major trophies during a 12-year spell in charge.
Bompastor has enjoyed similar success in France, leading Lyon to seven trophies over the past three seasons.
"I will give my all to this new project to meet the ambitions of the club, the staff and the players," said Bompastor in a club statement.
"I hope to live up to Emma's legacy and continue the work that has been done in recent years. Let the adventure begin."
Hayes, who has taken over as coach of the USA women's national team, signed off in style as Chelsea claimed a fifth consecutive English title on the final day of the season earlier this month.
Bompastor fell short of a fairytale ending at Lyon as they lost last weekend's Champions League final 2-0 to Barcelona.