The energy company has agreed a deal with Norwegian firm Equinor to capture 1.5m tonnes of carbon dioxide (CO2) annually and store it under the North Sea.
Peterhead is the last power station in Scotland to run off fossil fuels.
Some environmentalists have criticised the carbon capture technology.
They fear it gives big companies a licence to continue burning fossil fuels instead of phasing them out.
But Peterhead was Scotland's most polluting site in 2018 after problems at the Hunterston nuclear power station in Ayrshire caused demand for electricity from gas to rise significantly.
SSE has been attempting to install carbon capture technology at Peterhead power station since 2006 but no scheme has come to fruition so far.
Equinor is the Norwegian state-owned multinational energy firm.
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