Kasit, a former ambassador to the US, has supported the anti-government People's Alliance for Democracy (PAD), whose campaign occupied Government House for three months and the capital's main airports for more than a week.
His appointment has raised questions about Abhisit's commitment to reaching out to supporters of Thaksin Shinawatra, the former prime minister ousted in a 2006 coup and now convicted of corruption and living in exile. Thaksin remains popular with the poor rural masses.
In his inaugural address, Abhisit said he would restore Thailand's tourist-friendly image, damaged by six months of political turmoil.
The eight-day siege of Bangkok's airports last month stranded more than 300,000 travellers.
The 44-year-old's elevation to the prime minister's post came after a court dissolved the People Power party which lead the previous government and was packed with Thaksin's allies.
Korn, also 44, is an economist and former investment banker who headed Thailand's office of JP Morgan Chase from 1999 to 2004.
Kasit, 64, is a former ambassador to Japan, Germany, Indonesia and the former Soviet Union, but he has appeared several times as a guest speaker at the protests led by the PAD.
He praised the airport blockade as a "new innovation for public protests".
Suthep Thaugsuban, 59, has been appointed as deputy prime minister to oversee security matters, but he has been linked to corruption.
Suthep, secretary-general of the Democrat party, was accused in 1995 of distributing plots of land allotted for agricultural use by the poor to his associates. The scandal brought down the administration of the then prime minister, Chuan Leekpai.
Chavarat Charnvirakul, 72, a former Thaksin supporter who defected to the Democrats, has taken the interior minister's portfolio.
Chavarat was a deputy prime minister in the previous administration led by Thaksin's brother-in-law, Somchai Wongsawat.