Leverkusen sit ninth in the Bundesliga table heading into the winter break and, despite securing a third win in four league games by beating Hertha Berlin on Saturday, Heiko Herrlich has been relieved of his duties.
And the club have revealed that Bosz, whose successful 2016-17 campaign with Ajax led to a short-lived stint at Dortmund, which came to an end in December 2017, will take over in the new year, having signed a contract until 2020.
"Heiko Herrlich gave our team an important boost last year after a very difficult season," Leverkusen sporting director Rudi Voller said in a statement.
"Until the end we had the conviction and the will to make it with him as head coach. Unfortunately, a stagnation in the development of the team is no longer deniable."
Leverkusen sporting director Simon Rolfes added: "Bosz stands for offensive, fast-paced and inspiring football.
"He has always shown a special passion for working with young players, that's why he fits in very well with us."
Bosz took charge of Ajax in July 2016, and guided the Eredivisie club to the Europa League final – where they were beaten 2-0 by Jose Mourinho's Manchester United – and a second-placed finish in the Dutch top flight, before taking over at Dortmund.
A seven-match unbeaten run in the league saw Dortmund flying at the start of the campaign, but an eight-game winless streak and no victories in the Champions League group stage resulted in Bosz losing his job at Signal Iduna Park.