The 19-year-old arrives on a free transfer having signed a contract until 2025.
Braaf follows on from Sancho, who moved to the German club from City’s juniors in 2017, then broke into the senior England team on the back of performances for Dortmund before his high-profile transfer to Manchester United last summer.
Braaf, who plays on the wing, joined The Citizens from the academy of PSV Eindhoven in 2018, but has not played since suffering a knee injury at the end of 2020/21 on loan at Udinese Calcio.
Dortmund’s sports director Sebastian Kehl said they have been tracking the progress of Braaf, who he describes as a “great talent”.
“After more than a year out with injury, he will need time to regain his strength and establish himself,” Kehl added.
“We want to give him this time and introduce him gently.”
Dortmund also confirmed Friday the signing of Alexander Meyer from second division Jahn Regensburg as back up to first-choice goalkeeper Gregor Kobel.
Dortmund have already strengthened their squad by also signing Turkey midfielder Salih Ozcan from Cologne, as well as Germany centre-backs Nico Schlotterbeck from Freiburg and Niklas Suele from Bayern Munich.
Edin Terzic has been named head coach for next season after Dortmund parted company with Marco Rose.