Under the contract, the value of which wasn't disclosed, Rolls-Royce will supply its MT30 gas turbine engine, which produces 36-40 megawatts of power.
"We are delighted that the Republic of Korea Navy has selected the MT30 for the first ship in the FFX Batch II program," said Andrew Marsh, president of Rolls-Royce - Naval.
"The MT30 is the engine of choice to power the world's most advanced naval ships, where demand for power is increasing as more navies choose all-electric ships with sophisticated on board systems.
"We look forward to working with HHI, DSME and the navy in delivering what will be the world's first frigate to feature the MT30."
South Korea's FFX Batch II program includes eight ships.
Rolls-Royce said the MT30 engine for the ship will be built and tested in Britain prior to shipping to South Korea, where Hyundai Heavy Industries will integrate it into a steel enclosure before installation.