The appointment comes after current chief executive Brian Dames announced in December that he would step down at the end of this month.
Matjila, who is former chairperson of the National Energy Regulator of South Africa, will return to his position as a non-executive director of the Eskom board once a new CEO is appointed.
Eskom chairperson Zola Tsotsi paid tribute to Dames and his work at the helm of the power producer.
"Brian had successfully brought stability to Eskom and through his strong leadership, we were able to keep the lights on... Eskom is indebted to him for his life-long contributions to the company."
The process of appointing a new chief executive was still underway, with an executive recruitment agency being appointed to help find the right person for the job.
"The Board took the considered view that while
the company's executives are sufficiently competent for this position,
their pressing priority is managing the highly constraint electricity
system," Eskom said.
"The executives are however eligible and free to apply for the full-time position."
Dames' last day would be on Monday and Matjila would take up the acting CEO position from Tuesday.Dames was appointed chief executive of Eskom on July 1 2010, after serving Eskom in various management positions and as member of the executive committee in 2004.
He joined Eskom in 1987 as a graduate in training, according to Whoswho.
The news that Dames' resignation was widely met with regret.
At the time Public Enterprises Minister Malusi Gigaba's office said in a statement that Dames steered the company meticulously and with integrity.
"Despite the many challenges, he managed to keep the company stable."