The Belgian striker joins Borussia Dortmund as part of a combination of transfers that also cleared the way for Chelsea to recruit Olivier Giroud from the Emirates.
Chelsea signed Batshuayi for £33m from Marseille in the summer of 2016 and he has scored seven Premier League goals in 32 appearances.
After Arsenal confirmed they had completed a club-record move for Aubameyang, the Bundesliga outfit immediately replaced the Gabon international with a new centre-forward.
Batshuayi left the Chelsea team hotel on Tuesday, with the club giving the 24-year-old permission to travel abroad to agree terms with Dortmund. The deal reportedly includes a buy-out option after an initial six-month loan.
BVB leiht Michy #Batshuayi bis Saisonende vom @ChelseaFC aus!
— Borussia Dortmund (@BVB) 31 January 2018
Alle Infos: https://t.co/WUplWHl5b4 pic.twitter.com/za5nQaT2dT
"In order to reach my big goal, I want to play as much as I can and score many goals," said Batshuayi, who will don the No 44 shirt at the Signal Iduna Park. "In summer, the World Cup takes place."
BVB sporting director Michael Zorc said: "Michy is a young, very interesting striker, who impresses with a high scoring and his extraordinary at both Chelsea and in Marseille, in the Belgian league and the national team quality has already proved."
Michy #Batshuayi ist da! pic.twitter.com/W1bc41bkvA
— Borussia Dortmund (@BVB) 31 January 2018