Batshuayi made just 10 starts in all competitions for Antonio Conte’s side this term, but still managed to bag 10 goals from his 25 appearances in total and netted a brace in the 3-0 win over Newcastle on Sunday.
BVB were in the market for a new frontman after selling Pierre-Emerick Aubameyang to the Gunners earlier on Wednesday, which opened the door for Giroud to move to Stamford Bridge.
Dortmund sporting director Michael Zorc told the club’s official website: “Michy is a young, very interesting striker who boasts a good goalscoring record and has shown his extraordinary quality at Chelsea and Olympique Marseille, in the Belgian league and while playing for the national team.”
Batshuayi added: “In order to achieve my big objective, I want to play as much as possible and score many goals. The World Cup is taking place in the summer.”