The 22-year-old was in the Belgium squad which reached the quarter-finals of Euro 2016.
"I am delighted to sign for one of the biggest clubs in Europe and embark on the next chapter in my career," Batshuayi told the club website.
"I hope I can help Chelsea win many trophies during my time at Stamford Bridge."
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He said his Belgium team mates Eden Hazard and Thibaut Courtois, both Chelsea players, had told him many good things about the London club.
"This is a fantastic opportunity for myself and my family, I am looking forward to playing in the Premier League next season," Batshuayi added.
(Reporting by Ed Osmond; Editing by Clare Fallon)
