Babbel will continue to coach the Bundesliga team but is pleased the club have relieved him of some of his responsibilities so he can focus on his main task.
Mueller, who was sporting director of Schalke from 2006 to 2009, will now play a leading role in the club's transfer strategy.
"I enjoyed the job, but the additional workload was excessively high and I realised that I'm simply better suited to coaching," said Babbel.
"So at the start of the season I asked the club to step up the search for a sporting director. And I'm delighted they found such an excellent solution in the form of Andreas Mueller."
Chief executive Alexander Waldi said: "Andreas Mueller has convinced us with his ideas. We believe he can be a key component in bringing another piece of stability to Hoffenheim.
"We thank Markus Babbel for his commitment as director of football. We are certain that he can lead the team out of the critical situation we are currently in."