The historic event, held in front of the National Assembly building, was attended by an estimated 70,000 people.
The 18th presidential inaugural ceremony included a 21-gun salute and a performance from Korean rapper Psy, whose song Gangnam Style has been a global hit.
Australia's Governor-General Quentin Bryce was among the international dignitaries attending the ceremony.
In her inauguration speech, Ms Park took a strong stance on North Korea, demanding Pyongyang abandon its nuclear ambitions immediately.
The 61-year-old had campaigned on a promise of greater, "trust-based" engagement with Pyongyang, but observers say her hands have been tied by the international outcry over the North's February 12 nuclear test.
"North Korea's recent nuclear test is a challenge to the survival and future of the Korean people, and there should be no mistake that the biggest victim will be none other than North Korea itself," she said.
"I will not tolerate any action that threatens the lives of our people and the security of our nation," Ms Park said, while also promising to pursue the trust-building policy with Pyongyang she had promised.
"I will move forward step by step on the basis of credible deterrence," she said.
Focus on the economy
Ms Park was elected last year after promising to fix the country's slowing economy.
She made this the main focus of her inauguration speech, committing to job creation, expanded welfare and "economic democratisation" at a time when many Koreans are concerned with income and wealth disparity.
South Korea experienced an extraordinary economic revival from war-torn poverty after the 1950-53 Korean War.
The so-called Miracle on the Han has slowed in recent years, hit by the effect of the global downturn.
Ms Park promised "another miracle", saying her administration would look past Korea's traditional manufacturing base to build a "creative economy".
"At the very heart of a creative economy lie science and technology and the IT industry, areas that I have earmarked as key priorities," she said.
Ms Park promised to build a fairer market for small and medium-sized businesses to grow, an obvious warning to the huge, family-run conglomerates or "chaebols", such as Samsung and Hyundai that dominate the national economy.
"By rooting out various unfair practices and rectifying the misguided habits of the past which have frustrated small business owners... we will provide active support to ensure that everyone can live up to their fullest potential," she said.
More challenges ahead
As leader of Asia's fourth-largest economy, Ms Park faces significant challenges including the slowing economy and soaring welfare costs in one of the world's most rapidly ageing societies.
Despite its economic revival, Korea remains in many ways a conservative nation, where men still have a stranglehold over political and commercial power.
Ms Park will lead a country that is ranked below the likes of Suriname and the United Arab Emirates in gender equality.
She has taken office a little more than 50 years after her father, Park Chung-hee, seized power in a military coup.
Both her parents were eventually assassinated, and Ms Park says it has been strange for her to return to the national stage.
"When I was just 23 years old I assumed the unprecedented duties as our country's acting first lady," she said.
"That was because I had the responsibility to fill the void left by my mother's death at the hands of a North Korean terrorist."
Ms Park has never married or had children.