After a day of interviews, WHO's executive board chose UN veteran David Nabarro of Britain, ex-Pakistani health minister Sania Nishtar and senior Ethiopian politician Tedros Adhanom.
France's former foreign minister Philippe Douste-Blazy and Italy's Flavia Bustreo, a current WHO deputy chief, were eliminated.
The three finalists will campaign for votes among WHO's 194 member-countries before a final poll in May.
"This is an enormously important election," the director of Harvard University's Global Health Institute, Ashish Jha, told AFP.
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WHO may be the United Nations' most influential body, coordinating responses to pandemics like Ebola and Zika, but also setting standards for national healthcare systems including in advanced Western countries.
Since 2006, it has been led by Hong Kong-born Margaret Chan, whose tenure has suffered from accusations of inadequate transparency and accountability.
Those complaints boiled over with the 2014 Ebola epidemic in west Africa, when WHO was found to have missed glaring warning signs about the severity of the crisis that ultimately killed more than 11,000 people.
WHO officials often lament their funding constraints, but the Harvard professor said financing problems are caused by the fact that "donors don't fundamentally trust WHO to do a great job".
Among the criticisms of the Ebola response was that WHO deferred to governments in the region, notably Guinea, as they initially sought to downplay the dangers of the outbreak.
The editor of The Lancet medical journal, Richard Horton, told AFP the election was "make-or-break time" for the Geneva-based WHO, especially after the failures linked to Ebola.
Nabarro, 67, is an Oxford-educated doctor who has held a series of high-level WHO posts. With the Ebola crisis raging in August 2014, Nabarro was tapped to take over the botched UN response and won praise for helping contain the outbreak.
Among the top priorities listed on his campaign website is aligning WHO to respond outbreaks and emergencies.
Nishtar, the only woman in the group, has high-level experience within the UN but also founded and has led Heartfile, a respected non-profit focused on healthcare in Pakistan, possibly giving her the outsider credential that some say the agency needs.
Tedros, a former foreign and health minister, is also a renowned malaria researcher, applauded for expanding access to healthcare in Ethiopia.
He is being strongly backed by the African Union and, if elected, would be the first African to lead the global health body.
While experts urged WHO members to pick the most qualified candidate, they conceded that the lobbying ahead of the May poll will inevitably be highly politicised.
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