Favre, who has spent the last two seasons with French outfit Nice, will replace Peter Stoger as head coach of the Bundesliga outfit on a deal until the end of the 2019-2020 season.
"Coaching Borussia Dortmund is an exciting task that I'm delighted to take on. I'd like to thank the directors for the faith they've shown in me," Favre told the club's official website.
"We'll now work together on the new team. BVB is one of the most interesting clubs in Europe and I'm looking forward to returning to the Bundesliga, which I know extremely well and always kept an eye on during my two years in Nice."
Dortmund's sporting director Michael Zorc added: "The appointment of Lucien Favre as coach is an important aspect of our fresh sporting start this summer.
"He's highly regarded by us for the technical qualities that he demonstrated in impressive style many times throughout his spells with Hertha BSC and Monchengladbach in the Bundesliga, and more recently with Nice."