She will not be declared the official winner until Thursday, The New York Times reported. But Moon Jae-in, trailing with about 48 percent of the vote to Park's 52 percent with most of the vote counted, conceded.
"This is the victory of the people," Park told supporters. "This is a victory for the people's wish to overcome crises and revive the economy."
Park's father seized the presidency in 1961 in a military coup and ruled until his 1979 assassination by the head of the intelligence services. Moon, a human rights lawyer, was arrested as a student for organizing a protest movement against the elder Park.
President Obama released a statement congratulating Park. Obama called the relationship between the United States and South Korea a "lynchpin of peace and security in the Asia Pacific," adding "our two nations share a global partnership with deep economic, security, and people-to-people ties."
Park, 60, was the candidate of the governing Saenuri Party. She spent almost 20 years out of public life after her father's death but has since gained a reputation for honesty, the Times said.
The first woman elected president in South Korea, Park has promised to be a mother to the country.
"I have no family to take care of," she said during the campaign. "I have no child to inherit my properties. You, the people, are my only family, and to make you happy is the reason I do politics. And if elected, I would govern like a mother dedicated to her family."
The new president will succeed Lee Myung-bak, who is stepping down after his five-year term as required by law.