Sterlite Copper, which operates a 400,000-tonne-per-year smelter in Thoothukudi, was forced to shut its plant by Tamil Nadu state in May, and is estimated to have lost more than $200 million since.
Kumar replaces P. Ramnath, who led Sterlite for eight years. Under Ramnath, the smelter was ordered shut at least twice, including for an alleged gas leak in 2013.
Local residents and environmental activists have staged protests against the Sterlite copper plant over allegations of pollution as well as the earlier gas leak. Vedanta says the claims of pollution are false, without any factual basis. It also denied being the source of the gas leak.
The chief executive replacement comes amid a drawn-out legal battle over the smelter that could be complicated further by Lok Sabha elections that start on 11 April. The AIADMK and DMK, the two main political parties in Tamil Nadu, are against reopening of the Sterlite copper plant, increasing the likelihood that the shutdown will continue.
Vedanta won a judgment in December from India's Natural Green Tribunal (NGT) that would have cleared the way to reopen the smelter, but India's Supreme Court ruled in February that the environmental court did not have jurisdiction over the smelter.
"My tenure as CEO has been an eventful journey, and as is the case with any journey, there have been numerous ups and downs," Ramnath, who will continue as an adviser to the company, said in a statement.
Kumar, who will also oversee operations at Vedanta's Malco Energy Ltd and Fujairah Gold, has worked at Hindustan Zinc Ltd, Tata Steel Ltd and Adani Ports Ltd, in a career stretching over 29 years.
Kumar was also chief operating officer at Sterlite Copper in the past, the company said.
"It is an honour to be back in a place that feels like home," he said.