The Gelsenkirchen outfit announced that Jens Keller had paid the price for Schalke's inconsistent start to the season, which has seen the team take just eight points from seven matches, when he was dismissed earlier on Tuesday.
Di Matteo was confirmed as the club's new head coach and he will take charge of the team for the first time against Hertha Berlin on October 18.
The Italian has been without a club since he was sacked by Chelsea in November 2012, having led the Premier League side to a UEFA Champions League and FA Cup double in the 2011-12 campaign.
And Heldt believes the club have the right man to deliver success to the Veltins-Arena.
"With the coaching change we want to implement a new impetus," he told the club's official website.
"We are firmly convinced that Roberto Di Matteo will stabilise the team and manage to achieve our goals in the Bundesliga and the Champions League."
Heldt paid tribute to the job Keller has done in the near two years he was in charge but stated that the team's failure to maintain a high standard of performance meant a change was necessary.
"We should not forget that Jens Keller has done a good job in the past 22 months," he continued. "He took over the team in December 2012 in a difficult situation, led the team twice in the group stage of the Champions League and each time reached the knockout stage. He deserves the thanks of Schalke.
"[But] the achievements of the team in recent weeks have been repeatedly inferior and fluctuated strongly.
"Also positive approaches, such as the seven points [in the space] of a week with the icing on the cake the derby victory [over Borussia Dortmund] did not show any lasting effect.
"We have lacked the necessary consistency to achieve our athletic goals. Therefore, we decided to make a change."
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