Bosz, 56, took over in January 2019 and guided them to a fourth-place finish. This season, they sit seventh, nine points behind leaders RB Leipzig, before Sunday's away match at bottom side Paderborn as the league resumes this weekend after the winter break.
Under Bosz, Leverkusen managed back-to-back league wins over Bayern Munich and Schalke last autumn.
However, poor performances meant they failed to reach the knock-out stages of the Champions League after finishing third in their group and lost three of their final four games of 2019.
"We greatly appreciate Peter Bosz's daily work for Bayer," said club chairman Fernando Carro in a statement.