The 19-year-old moved to Germany from boyhood club Birmingham in 2020 but has long dreamt of playing for the LaLiga giants.
Dortmund confirmed in a statement last week Real had agreed to pay an initial 103m euros ($A164m) to land Bellingham.
Now Real have confirmed the deal is complete.
"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," their statement read.
"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."
Bellingham himself paid tribute to Dortmund on Instagram, writing: "Where to start, for the last three years Borussia Dortmund has been the biggest part of my life.
"I joined as a 17 year old boy and am leaving as a man. I cannot thank this club enough for everything it's done for me.
"The opportunities, the experiences, the highs and even the lows. All of it has been part of what has been a great development both as a human and a player.
"I am honoured to have represented this football club as often as I have, I'd like to thank all the players, managers, bosses and members of staff that have played a role in my time at the club.
"I'll always keep a place for BVB in my heart and will never forget the impact the values of the club has had on my life. Einmal Borusse, Immer Borusse. I wish the club nothing but the best for the future! Heja BVB!"
Bellingham was recently named Bundesliga player of the season after his starring role for Dortmund, who missed out on the title in agonising fashion on the final day of the campaign.
He scored his first England goal in their World Cup win over Iran but is absent from the squad to face Malta and North Macedonia in the upcoming Euro 2024 qualifiers due to injury.
He has long dreamt of a move to the 14-time European champions and recently told the PA news agency he sees the Champions League as "the biggest stage".
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