For the first time ever, the US domination of the World Bank is being challenged - but the American is still the favourite to become the next boss.
On Friday, Colombia's Jose Antonio Ocampo pulled out of the race, calling the selection process a "political exercise".
Either Mrs Okonjo-Iweala or Dr Kim will replace Robert Zoellick, who has run the World Bank since 2007.
By convention, the US has always held the top job at the World Bank since it was founded in 1944.
The top job of its sister organisation, the International Monetary Fund, has also always gone to a European but there has been much pressure from emerging economies to open the processes of both organisations to competition.
"It's no longer in the smoke-filled rooms of Europe and the United States that the spoils are shared," South Africa's finance minister Pravin Gordhan said on Monday.
But he conceded that it was likely the "established powers" would make the final decision when the 25-member World Bank board meets to vote.
European countries are likely to support the US bid as has happened in the past. Europe and Japan together have 54% of the votes to appoint the bank's president.
The next president of the World Bank will oversee a staff of 9,000 economists and development experts and and a loan portfolio that hit $258bn (£163bn) last year.
''Unselfish decision''
President Barack Obama's choice of Dr Kim came as somewhat of a surprise but the 52-year-old is a leading figure in global health.
Born in Seoul, he moved with his family to the US at the age of five and became president of Dartmouth College in 2009.
A doctor and former director of the HIV/Aids department at the World Health Organization, he also co-founded the health charity Partners in Health in 1987.
The other candidate, Mrs Okonjo-Iweala, was a managing director at the World Bank until last year, when she left to take up her current position as finance minister.
Mr Ocampo was the third candidate on the shortlist for the presidency, but pulled out on Friday.
"It is clear that this is not based on the merits of the candidates but is a political exercise," he said.
Mr Ocampo, who is a professor at Columbia University, said that he would now support Mrs Okonjo-Iweala "to facilitate the desired unity of the emerging and developing economies around one candidate".
Mrs Okonjo-Iweala thanked Mr Ocampo for his "unselfish decision" to withdraw.
This year's vote is the first time the World Bank has had to choose between candidates since its creation more than 60 years ago.
US is in for rig... not base on Merit but on "who knows who" or "god-fatherism" Hypocrites Indeed
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