Zinedine Zidane’s men signed Reinier for €30m from Flamengo in the January transfer window but he is yet to make an appearance for the Los Blancos first team.
Reinier made three appearances for the Real Madrid B team in Segunda B1, scoring two goals, before the season was halted in March due to the coronavirus pandemic.
The 18-year-old becomes Dortmund’s third summer signing after Thomas Meunier and Jude Bellingham.
"Reinier is a player who possesses enormous talent and can be deployed in various attacking positions," said Borussia Dortmund sporting director Michael Zorc.
"We've been keeping tabs on the lad for over two years; in addition to his outstanding technical qualities, he also boasts a strong physical presence.
"Following the long break from competitive football, we'll give him the necessary time to adapt to professional football in Germany and he can then be an additional option for us going forward."
Reinier said: "I am happy to be with BVB now. The club is known for betting on young players and making them better.
"I want to learn a lot here, play a lot and help the team to be successful. I hope that we will have many happy moments together."
Reinier will hope to follow in the footsteps of Achraf Hakimi, who enhanced his development at the Signal Iduna Park on loan for two seasons from Real Madrid, before getting sold to Inter Milan for €40m this summer.
