South Africa is the only country on the continent with a civilian nuclear industry, and its two reactors have been in service for more than 30 years.
The Koeberg nuclear power plant, located outside Cape Town, produces 1,860 megawatts contributing about four percent of the national power output.
Eskom in a statement that its "spent fuel pools are essentially full in 2020 and for this reason a project was initiated to create additional space".
It said it would start to transfer "some of the used fuel" to dry storage casks.
The casks have already been procured and "are currently on site" and Eskom said it was "in the process of preparing to transfer used fuel from the... pools into these casks".
Eskom said it opted for the dry storage solution as it is widely used in the nuclear industry across the world.
"Koeberg is the only nuclear power plant in Africa, and hence the option of a centralised wet storage repository is also not financially viable, nor is it technically viable to increase the size and storage capacity of the Koeberg spent fuel pools," it said.
Koeberg was originally set to be mothballed in 2024, four decades after its inception, but it is being upgraded and it is now expected to operate until 2044.
Environmental campaigners have warned against the nuclear project.
"It is incredibly short-sighted for the government to pursue extending Koeberg's lifespan, potentially at the expense of our safety," Melita Steele, Greenpeace Africa's Climate and Energy Campaign Manager said Tuesday.
"Not only are South Africans going to have to fork out more money for more storage for high-level radioactive waste, but there is also no long-term solution for this waste, which can remain radioactive for hundreds of thousands of years," Ms Steele said.
Currently, 90 per cent of the country's electricity is generated from coal-fired stations.
The government last year dropped controversial plans to build new nuclear power stations, deals that had been initiated by former leader Jacob Zuma and that could have bankrupted the country to enrich his allies.