Braaf announced on Thursday that he would leave City, where he was offered limited first-team chances after joining from the PSV youth academy in 2018.
The 19-year-old was previously linked to a move to Dortmund in 2020 but ended up joining Udinese on loan, scoring once in four appearances before a knee ligament injury ruled him out for a year.
Dortmund confirmed on Friday that they have captured the promising winger on a three-year deal, Braaf following in the footsteps of Jadon Sancho and Jamie Bynoe-Gittens, who traded City for the Bundesliga side.
Braaf's arrival marks another new addition for Dortmund, who signed Karim Adeyemi to help replace the City-bound Erling Haaland, while also bringing in Niklas Sule, Nico Schlotterbeck and Salih Ozcan.
"Jayden, whose development we have been following closely for years, has shown in the past that he can be a difference player with his pace and talent," soon-to-be sporting director Sebastian Kehl said.
"After more than a year out through injury, he will certainly need time to regain his former strength and fully establish himself in men's football.
"We want to give him this time and gently introduce him. If Jayden masters the phase ahead of him and stays clear, we have a great talent on board in him."
Dortmund, who appointed Edin Terzic as Marco Rose's successor for the next term, have also signed Alexander Meyer on a two-year contract from 2. Bundesliga side SSV Jahn Regensburg on a free transfer.
Meyer is expected to be the second-choice goalkeeper behind Gregor Kobel following the departures of Marwin Hitz and Roman Burki.
"Alexander Meyer convinced us both in terms of sport and personality. In him, we get a very experienced goalkeeper who exudes calmness and has shown in recent years as a regular keeper in Regensburg that he has high quality," Kehl said.
"He was undoubtedly one of the strongest goalkeepers in the 2nd Bundesliga in recent years.
Meyer added: "When a club like BVB calls, I don't have to think twice. From a sporting point of view, they're an absolute top team, and there's no need to talk about the atmosphere in the stadium.
"Just thinking about the Yellow Wall gives me goosebumps. I'm really looking forward to the new task and also to being part of the BVB family."