He has signed a five-year deal that will take him through to the summer of 2024 and will be reunited with former head coach Lucien Favre, who he worked with at Borussia Monchengladbach.
Dortmund finished second in the Bundesliga in 2018-19 after taking a commanding lead but slipping behind eventual winners Bayern Munich , and despite taking the fight to the final day, they could not climb above their rivals.
Since that disappointment, they have been quick to reinforce, and have swiftly moved to improve an area of identified weakness - left-back.
Schulz, 26, is a Germany international and a forward-thinking full-back often deployed as a wing-back, scoring two goals and registering nine assists in 37 appearances across all competitions this season.
Dortmund have been left short at on that side of defence with injuries to Real Madrid loanee Achraf Hakimi and Abdou Diallo - a right-back and a centre-back by trade, but both able to cover at left-back - leaving 31-year-old Marcel Schmelzer to hold the fort, along with the defensively-suspect Raphael Guerreiro, who is much more comfortable on the wing.
The defender represents their second signing of the summer, after making Spanish striker Paco Alcacer's loan deal from Barcelona a permanent one.
The forward impressed this season, hitting 18 goals in 26 Bundesliga games and also discovering a talent for taking free-kicks.
Links to wingers Julian Brandt and Thorgan Hazard have also emerged as they seek to replace the outgoing Christian Pulisic, who is bound for Chelsea.
They will be hoping to keep up with an already-active Bayern in the market, who have sealed deals for French defenders Lucas Hernandez and Benjamin Pavard from Atletico Madrid and Stuttgart, respectively, as well as young Hamburg striker Jann-Fiete Arp.