Gross, formerly with FC Basel, took over immediately on a contract that runs until 2011.
"I am here to save what is left to save," the 55-year-old Gross said in a hastily arranged news conference.
"I want to take the team back on to the path of success," he added, before leaving for an evening training session with his players.
"It was a moving year and we achieved amazing things," Babbel told reporters after the club announced his sacking in a statement.
"I wish the new coaching staff all the best and hope they will find the button to reignite the team. I did not find that button."
Despite their poor Bundesliga form, Stuttgart can still reach the Champions League knockout stage with a home win over Romania's Unirea Urziceni on Wednesday.
GOMEZ LOSS
This season, the rookie coach, who is still studying for his coaching licence, failed to replicate last year's form and the team have won only two of their matches so far.
Fans booed and jeered the Stuttgart players when they arrived for the Bochum clash and an 89th-minute equaliser by the visitors prompted some in the stands to unfurl a banner reading: "You have just used up your credit."
Babbel called the fans' reaction unacceptable.
"I have been in this business a long time but have never seen anything like it. We had two 19-year-old players on the pitch who were scared. That was because of the fans' behaviour," he said.
