She arrived Sunday for a four-day state visit.
The agreement, signed following talks between Patil and South Korean President Lee Myung-bak, would allow Seoul to participate in the construction of nuclear power plants in India, South Korea's Yonhap News Agency reported.
There are now 20 power-generating nuclear reactors in India but the country plans to build about 40 more by 2032. South Korea would join Russia, France and the United States in those projects.
The agreement comes as South Korea's state-run Korea Electric Power Corp. seeks to enter the Indian market. South Korean firms already are involved in a $18.6 billion project to build four atomic power plants in the United Arab Emirates, the report said.
In her talks with Lee, Patil shared the view that cooperation between the two countries has increased in all areas and agreed to further expand it in political, security and defense industry sectors, Lee's office said. The two sides also agreed to improve their free trade agreement.