Bosz, 53, arrives from Ajax after leading the Dutch side to the final of the Europa League, where they lost 2-0.
"Peter Bosz is the new BVB Head Coach. Contract will last until 2019," Dortmund said on their Twitter account, announcing the appointment.
Bosz, 53, arrives from Ajax after leading the Dutch side to the final of the Europa League, where they lost 2-0 to Manchester United last month.
Briefly a player in Germany with Hansa Rostock in the 1990s, he replaces Thomas Tuchel, who was sacked despite Dortmund winning the German Cup -- their first major silverware in five years -- and finishing third in the Bundesliga in the season just finished.
"Beyond our sporting ambitions, the feeling we got straight away that we can build something together here was decisive," said club CEO Hans-Joachim Watzke at a press conference.
German media reports say Dortmund agreed to pay Ajax five million euros ($5.6 million, £4.4 million) to bring in Bosz, with SID, an AFP subsidiary, saying the compensation paid is "the highest in the history of the Bundesliga" for a coach.
"I am proud to be able to work at such a big club," said Bosz in perfect German.
"Borussia is one of the 10 biggest clubs in Europe, with a young team and the legendary 'Yellow Wall'," added the new coach in reference to the vast South Stand at the Signal Iduna Park.
Switzerland's Lucien Favre, formerly in charge at Borussia Moenchengladbach, had been linked with a return to the German game with Dortmund but his current side Nice refused to let him go.
Giovanni van Bronckhorst, whose Feyenoord side pipped Ajax to the Dutch title, had also been linked with the Dortmund job, as had Cologne's Peter Stoeger and David Wagner, a former member of the BVB coaching staff who has just taken Huddersfield Town into the English Premier League.
But instead Bosz got the nod, ending his one-season stint at Ajax, where he arrived last year after a brief spell in Israel with Maccabi Tel Aviv.
He had previously been in charge at Vitesse Arnhem, while his playing career also took in spells in France and Japan and saw him win eight caps for the Netherlands as a midfielder.
Dortmund finished second in the Bundesliga behind Bayern Munich in Tuchel's first campaign in charge but he was said to be deeply unhappy at the decision to sell Mats Hummels, Henrikh Mkhitaryan and Ilkay Gundogan last year.
His side never seriously challenged for the league title in the season just finished, and while they beat Eintracht Frankfurt in the German Cup final, they went out of the Champions League in the quarter-finals at the hands of Monaco in April.
That tie was overshadowed by a bomb attack on the Dortmund team bus ahead of the first leg, which Monaco won 3-2 at the Signal Iduna Park.
The decision to play that match just 24 hours after the attack, in which defender Marc Bartra was badly injured, reportedly increased tensions between Tuchel and Watzke.
Dortmund eventually lost the tie 6-3 on aggregate.