The right-back,19, has agreed a five-year contract with the Bundesliga club and arrives on a free transfer after running down his deal at Barca.
Morey, who was also reportedly a target for Juventus and Manchester City, missed the entire 2018-19 season after suffering a serious knee injury but is now fully fit and set to be involved in Dortmund's pre-season.
Get to know our newest signing, Mateu Morey, a bit more! 🇪🇸💎 pic.twitter.com/ZRdylybG0O— Borussia Dortmund (@BlackYellow) July 2, 2019
"Borussia Dortmund are a fantastic club that place a lot of emphasis on youth. I'm confident that, with my individual qualities, I will have a lot to offer the club in the years to come," Morey said.
"I want to integrate myself quickly, support my team and, above all, learn the language. Doing the latter will certainly make everything easier!"
Morey was part of Spain's Under-17 side that won the European Championship and triumphed in the 2016-17 UEFA Youth League with Barcelona.
"Mateu Morey is a top defensive talent from the Barcelona academy, who possesses exceptional technical quality," Dortmund sporting director Michael Zorc said.
"We see this transfer as one for the future and we are greatly looking forward to developing Mateu as part of our first-team squad."
Morey's arrival continues a busy close-season at Dortmund following the signings of Mats Hummels, Nico Schulz, Thorgan Hazard and Julian Brandt.