The MoUs are aimed at furthering defence educational exchanges and extension of mutual logistical support for the navies of both countries, Defence Ministry officials said on Friday.
Singh met his South Korean counterpart Jeong Kyeongdoo on Thursday during his three-day visit to the country, which will end on Friday.
"Had productive discussions with the Minister of National Defence of RoK, Mr Jeong Kyeong-Doo, during bilateral meeting. The ongoing defence cooperation engagements have made good progress in recent years. We agreed that there was great potential to further enhance these ties," he tweeted.
According to a ministry official, the two leaders had a comprehensive review of bilateral defence co-operation and noted that defence co-operation lies at the heart of the Special Strategic Partnership between India and South Korea.
Ongoing co-operation at service-to-service level and prospects for enhanced co-operation between defence industries of India and Korea were also discussed apart from exchange of views on regional and international developments of mutual interest.
Earlier, Singh paid homage at the National Cemetery of Korea and also visited the War Memorial where he presented a copy of the citation received by the Indian 60th Para Field Hospital for its exceptional contributions during the Korean War.
"Visited the War Memorial at Seoul in Republic of Korea today. The sacrifice and dedication of the UN forces and veterans in the Korean War will never be forgotten," Singh wrote in another tweet.
( With inputs from IANS )