Park also accepted the resignations of the chief of national security as well as her spy chief, presidential spokesman Min Kyung-Wook announced.
Ahn Dai-Hee, 59, is to replace outgoing Prime Minister Chung Hong-Won, who offered his resignation last month over the April 16 ferry disaster, which claimed around 300 lives.
"We believe that he is a right person to strongly push ahead with reforming government organs, correcting wrong practices and eventually transforming the country", the spokesman said.
Both Nam and Kim came under criticism over their inaction when the disaster struck.
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Ahn still needs parliamentary consent to officially be declared as prime minister, but this is a formality because the ruling Saenuri Party has majority status in the National Assembly.
Park's popularity ratings have slumped in the aftermath of the Sewol tragedy and her ruling Saenuri Party is greatly concerned over the political fallout from the disaster on June 4 local elections.
Parents and relatives of the missing and the dead have blasted the response to the sinking, saying delays in launching the rescue had cost lives.
There has also been rage over perceived corruption and lax safety standards that may have led to the disaster, with claims that the ferry was overloaded and that the passenger list was inaccurate and incomplete.
The polls are the first nationwide elections since President Park Geun-Hye took office 16 months ago. They are widely seen as a referendum on her performance leading the country.
As of today morning, a total of 288 passengers have been confirmed dead, most of them students on a school trip, with 16 others still unaccounted for.