The social security system of Korea is mainly composed of National Health Insurance Service (NHIS) and public pension programs. The NHIS covers the whole population as a compulsory social insurance system. Also, everyone residing in Korea is subject to the compulsory coverage of public pension program.

Website: https://www.nhis.or.kr/static/html/wbd/g/a/wbdga0101.html/

Foreign registration is a prerequisite to enrollment in the social security program in Korea. All foreigners intending to stay in Korea for more than 90 days after entry have to register as a foreigner to a Korean Immigration office. You have to visit your local immigration branch office(Ulsan) with the documents needed. You can be assisted by the staff at the Center for International Affairs.

It takes approximately 1 month to get your foreigner registration card after applying. If you think that you can’t get a foreign registration card before the first day of your employment, it is recommended for you to prepare private travelers insurance until your foreigner registration process is completed.

The foreign registration procedure is below. You can find more information on the Korean government website for foreigners.
http://www.hikorea.go.kr > Information > Immigration Guide)