The 53-year-old former Ajax boss succeeds Tuchel after leading the Eredivisie giants to the UEFA Europa League final and a second-placed league finish last season.
The Dutchman has signed a two-year-deal with the five-time Bundesliga champions, who finished third last season before beating Eintracht Frankfurt 2-1 in the DFB Cup final.
Bosz only spent one year in charge of Ajax but greatly enhanced his reputation as a coach who is able to bring the best out of up-and-coming players whilst promoting an attacking brand of football.
In contrast to his own playing days - when the former Feyenoord man was a hard-tackling defensive midfielder - Bosz likes his teams to express themselves. His management style is inspired by Ajax and Barcelona legend Johan Cruyff, and his preference for high-energy, aggressive pressing in a 4-3-3 system no doubt caught Dortmund’s eye.
Bosz's young Ajax side came up just short in the Dutch league last season when they finished second by a point to a Feyenoord team managed by Giovanni Van Bronckhorst.
Their hopes of claiming the league title were hampered by a thrilling but energy-sapping European campaign, during which they were beaten by Rostov in the UEFA Champions League play-off round before topping their UEFA Europa League group.
It was in the knock-out stages of the latter competition that Bosz's troupe really excelled. Having seen off Legia Warsaw and Copenhagen, Ajax turned on the style in the first leg of their quarter-final tie against Dortmund’s local rivals Schalke.
The visitors escaped from Amsterdam with just a 2-0 defeat before producing a brilliant second-leg display, only for Ajax to go through 4-3 on aggregate after scoring two goals in extra-time.
The Dutch outfit had a similarly dramatic semi-final against Lyon – winning 4-1 at home and losing 3-1 away – before being outmuscled in a 2-0 defeat to Manchester United in last month's final in Stockholm.
A fluent German speaker, Bosz had a brief spell in Germany as a player with Hansa Rostock in 1998 before twice managing Heracles in the Netherlands and serving as technical director of Feyenoord.
Before taking the top job at Ajax, the ex-Dutch international coached Vitesse Arnhem between June 2013 and January 2016. During his time there he led the club to fifth in the Eredivisie and qualification for the Europa League despite once again working with a youthful squad.
Following a brief spell in charge of Israeli side Maccabi Tel Aviv and a successful year at home, Bosz will now get the chance to lead Dortmund into the Champions League and try to build a team capable of dethroning Bayern Munich in the Bundesliga.