Park Geun-hye, whose father ruled South Korea for 18 years, became the country's first female president on Wednesday, narrowly beating her opponent in one of the most divisive elections for years.
Both Park and Moon said they would seek greater engagement with the North, although Park may have benefited from her demand that the regime abandon its nuclear and ballistic missile programmes.
Park, who said she had never married or had children so she could devote her life to public service, will inherit a formidable array of economic problems when she takes office on 25 February.
Inequality and youth unemployment have increased under Lee, who by law cannot seek a second term, and the economy is forecast to grow this year at its slowest pace since 2009, reports the Guardian.