The 22-year-old right-back arrives after two seasons on loan at La Liga side Girona, helping them to a surprise third place finish last season.
During his time in Spain, the defender scored two goals and assisted 12 more in 59 La Liga games.
Sebastian Kehl, Dortmund's sporting director described Couto as "a very exciting player".
"His development in Spain was remarkable, and yet he has lots of potential to go even further, which makes him exactly what we wanted for this position."
Since making his debut for Brazil aged 21, Couto has made four appearances in the yellow shirt of the Selecao.
He joined Man City in 2020 aged 17 from Coritiba FC on a five-year deal for a six million euro fee but never appeared for Pep Guardiola's side.
"For me it’s a dream come true," said Couto in Dortmund's press release.
"Borussia Dortmund is a special club. Every child in Brazil knows how great this club is, knows the fans, and is fascinated by the 'Yellow Wall'.
"I can’t wait to wear the BVB shirt for the first time and experience the power and emotions in this brilliant stadium."
Couto is Dortmund's fourth major summer signing after striker Serhou Guirassy and defender Waldemar Anton, both from Stuttgart, and veteran Germany midfielder Pascal Gross.
