The company said the decision followed careful consideration and extensive consultation with stakeholders, including the SA government.
It believes the power station will no longer be viable following completion of a $2.4 billion electricity interconnector between SA and NSW in mid-2026.
AGL chief operating officer Markus Brokhof said the closure was not an easy decision.
"The economic situation of the Torrens Island Power Station was very critical," he told reporters on Thursday.
"We are losing money with this power station in the current environment."
Mr Brokhof said the closure was unrelated to the recent shareholder approval to install four new directors on the company's board as part of Mike Cannon-Brookes' efforts to influence the future direction of Australia's biggest power producer.
The directors had all been proposed by the billionaire's private company Grok Ventures after he amassed an 11.3 per cent stake in AGL, making him its largest shareholder, in a bid to fast-track phasing out coal and transitioning to renewables.
Mr Brokhof said it was also too early to tell how many of the 120 workers at the Torrens Island station would be made redundant.
"The jobs of today are not the jobs of tomorrow. We will make sure there's not only a proper energy transition but also a proper transition of our workforce," he said.
"We will have to see in the upcoming months and years what kind of jobs we can keep, what kind of redundancy we have on this site."
But the Australian Services Union said AGL's announcement came as a shock and called on the company board and Mr Cannon-Brookes to step up and take responsibility for those workers at risk.
"The past few months have been a daunting time for all workers in energy and today's announcement will be a a shock for many, especially so close to the Christmas period," union state secretary Abbie Spencer said.
"We will be working with our members and other stakeholders to ensure the best possible outcome for all workers at Torrens Island."
The Torrens Island B station opened in 1976, providing 800 megawatts of electricity for SA consumers.
However, the company mothballed the first of four generating units in October last year, after years of increased solar and wind energy supplies.
The remaining three units will be retired on June 30, 2026.
AGL said the decision was not expected to impact its profit forecasts this year or over the longer term.
Over the past four years, the company has invested $475 million in energy projects on Torrens Island, including the 210 MW Barker Inlet Power Station, which opened in 2019, and the 250 MW Torrens Island battery, which is expected to be operational next year.
SA Energy Minister Tom Koutsantonis said the previous state Liberal government's decision to build the interconnector with NSW had killed off the Torrens Island B power plant.
"The previous government deliberately designed the interconnector to displace SA gas with NSW coal," he said.
"I don't blame AGL for this decision. It's a decision that the economics of the interconnector was always going to make. We all knew this was coming."
However, Mr Koutsantonis remained confident SA would have enough power to cover periods of peak demand, thanks to the construction of a new generator in the state's mid-north, renewable energy supplies and access to power through interconnectors with both NSW and Victoria.