The move was hailed by two major exporters to South Korea - luxury carmaker Bentley and the Denby Pottery Company.
"My priority is to make sure that British businesses are fully prepared for Brexit," International Trade Secretary Liz Truss said in a statement.
Truss signed the agreement with South Korean Trade Minister Yoo Myung-Hee.
"Today's signing of the FTA (Free Trade Agreement) will remove much Brexit uncertainty out of our long, valuable economic partnership," Yoo said.
It is Britain's first post-Brexit trade deal in Asia and follows similar agreements with nations including Chile, Iceland, Norway and Switzerland.
Britain is scheduled to leave the bloc on October 31.