"We thank Jude for three years of passion for Borussia Dortmund," CEO Hans-Joachim Watzke told the Bundesliga club's website.
"It was a fantastic time together.
"We would also like to thank Real Madrid for the fair and constructive discussions."
Bellingham's most recent season delivered a total of 14 goals across all competitions, with the midfielder also contributing seven assists.
He has established himself as a regular in Gareth Southgate's England side, earning 24 senior caps following his debut against the Republic of Ireland in November 2020.
His first goal for the Three Lions came in the 6-2 victory over Iran in their opening game of the 2022 World Cup in Qatar.
Real confirmed that Bellingham's presentation ceremony will take place at the Santiago Bernabéu on Thursday.
It's been a meteoric rise for Bellingham following his debut for Birmingham in August 2019. He became the club's youngest ever first team player after appearing in their Carabao Cup contest against Portsmouth at 16 years and 38 days old.
Further signings are expected in Madrid this summer. They are also on the lookout for a Karim Benzema replacement, with the striker departing for Saudi Pro League champions Al-Ittihad at the beginning of June.