"We have taken a decision to permanently shut down the plant and today issued government orders to do the same," Edappadi K Palaniswami, chief minister of the southern state of Tamil Nadu said in a statement after meeting officials, including from the pollution department.
Residents and environmental activists have long demanded a shutdown of the copper smelter, India's second-biggest with an annual production of more than 400,000 tonnes, citing air and water pollution.
Vedanta has denied the accusations of pollution.
"We are finally free, we could have been happier if so many people had not died. This is for all of them," Muthu Pandi, a driver who had come to see the plant being shut, told Reuters.
The district's main administrative officer, called the collector, supervised the sealing as the crowd whistled and cheered from behind police barricades placed 50 metres away from the entrance. They shouted "Long live the collector," as the collector's car departed.
In the heart of the city, locals gathered near an electrical appliances showroom to watch the news on TV channels.
The plant, in the coastal city of Thoothukudi, has been shut since late March for maintenance and pending a renewal of its licence, even as residents continued largely peaceful protests demanding it be shut for good.
The opposition escalated on Tuesday when thousands of people marched towards a government office on the 100th day of the protest. Ten people were killed in police firing that day; three more died in subsequent days.
Vedanta says it has already evacuated about 3,500 employees from the plant site due to the tensions.