Former Tottenham Hotspur boss Christian Gross was named as Babbel's successor on Sunday evening and the 55-year-old has signed a contract until June 30 2011.
"I am here to save what still has to be saved," said Gross. “I want to get the team back on the road to victory."
Stuttgart need to beat Romanian champions Unirea Urziceni at home on Wednesday to reach the knock-out stages of the Champions League.
The 37-year-old Babbel was sacked less than 24 hours after his side drew 1-1 with Bochum, which left them third from the bottom of the German league with just two wins to their credit all season, and 12 points from 15 games.
"I wish the new coaching team all the best,” Babbel said. “I hope they find the way to get the best out of the team so they can play well again - I never found it."
A group of several thousand angry Stuttgart fans, demanding Babbel's resignation, squared off with police wearing riot gear outside Stuttgart's Mercedes-Benz Arena on Saturday after the draw with Bochum.
Despite being crowned German champions in 2007, Stuttgart have now gone eight league games without a win. Babbel, who took charge in November 2008, is the fourth Bundesliga coach to be sacked this season.
He joins Marcel Koller (Bochum), Dieter Hecking (Hannover 96) and Lucien Favre (Hertha Berlin) who also were dismissed by top-flight clubs here.
The departing boss had to be escorted away from Stuttgart's ground by police on Saturday and the ex-Liverpool defender admitted he was shocked by his treatment from his own fans.
"I had never experienced such scenes as I did on Saturday," said Babbel who admitted he was disturbed by such behaviour in the wake of Robert Enke's tragic suicide on November 10.
"Even the so-called football millionaires do not deserve to be subjected to so much hate and even murder threats,” he added. “After the Robert Enke tragedy many people spoke up and talked about what we had to learn from this. But what happened on Saturday shows me that it is all just hypocrisy."