Bosz, 57, has been replaced by former Germany Under-18 coach Wolf, 39, until the end of the season with Leverkusen currently sixth in Germany's top flight.
Wolf won the second division title with Stuttgart in 2016/17, but was sacked after a season at Hamburg after failing to get them back into the Bundesliga in 2018/19.
"With the new coaching team, we want to turn things around and again take the path to success that we had left," said Leverkusen's sporting director Simon Rolfes.
"Even as a very young coach, Hannes Wolf has impressed with big clubs and was particularly convincing through his promotion to the Bundesliga with VfB Stuttgart."