The teenager, who had been linked with several major European clubs, joined Dortmund from Birmingham City in 2020 for 25 million pounds, becoming the most expensive 17-year-old in football history.
He quickly became a regular in the Dortmund side, anchoring the midfield and starting more than 30 Bundesliga games in each of his last two seasons in Germany.
England manager Gareth Southgate made Bellingham the youngest English player to represent his country at a major tournament during the 2021 European Championship.
He soon became a permanent fixture in England's midfield, playing all five games at the World Cup in Qatar where they were knocked out in the quarter-finals by France.
Bellingham was linked with Premier League clubs who wanted to bring him home, including Liverpool whose manager Jurgen Klopp said they were forced to pull out of the race to sign him due to his price tag.
At Real Madrid, he will join a side rich in young midfield talent in Federico Valverde (24), Eduardo Camavinga (20) and Aurelien Tchouameni (23) as the club look to build for the future and replace long-time stalwarts Toni Kroos (33) and Luka Modric.
The variable transfer compensation will be a maximum of around 30% of the initial fee based on Bellingham's performances and sporting success Real Madrid enjoy, Dortmund added.
