The 19-year-old has signed a six-year contract at the Santiago Bernabeu and will be presented as a Real Madrid player on Thursday.
Bellingham departs Dortmund after three years at the club, making 132 appearances, scoring 24 goals and winning the DFB-Pokal in the 2020/2021 season.
The former Birmingham City youngster was named the Bundesliga's player of the season this term after Dortmund missed out on the title to Bayern Munich on the final day.
Real Madrid released an official statement announcing the deal on Wednesday, which reads: "Real Madrid CF and Borussia Dortmund have agreed on the transfer of the player Jude Bellingham, who will remain linked to our club for the next six seasons."
"Tomorrow, Thursday, June 15, at 12:00 noon at Real Madrid City, the presentation ceremony for Jude Bellingham as a new Real Madrid player will take place. Next, Jude Bellingham will appear before the media."
In a farewell message to Dortmund fans, the England international said: "Thank you to everyone at BVB and to the fans for everything over the past three years.
"It's been an honour to wear your jersey so many times, in big and small moments. Even though I look forward to my next destination, I will never forget the journey there. Once Borussia always Borussia. All the best for the future."
Dortmund chief executive Hans-Joachim Watzke added: "We thank Jude for three years of passion for Borussia Dortmund. It was a fantastic time together.
"We would also like to thank Real Madrid for the always fair and constructive discussions."
