The race to succeed Hong Kong-born Margaret Chan as the UN's global health boss will be decided by secret ballot among WHO member-states in Geneva.
Chan's decade-long tenure which ends on June 30 was notably marred by the fiercely-criticised response to the Ebola epidemic in West Africa.
WHO was accused of missing key warning signs about the severity of an outbreak that began in December 2013 and ultimately killed more than 11,000 people.
"When it happens the world will turn to the WHO for guidance and for leadership. We need to be sure it is up to the task," he told the Swiss Press Club.
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The finalists are former Ethiopian health minister Tedros Adhanom, British doctor and UN veteran David Nabarro and Pakistan's Sania Nishtar, also a former health minister who too led a respected non-government health organisation.
The three are bidding to head perhaps the most influential United Nations agency, charged with emergency response and shaping baseline policies for treatment of major health challenges.
Nabarro has been buoyed by massive support from his native Britain and has touted his intimate knowledge of the UN system.
Nishtar is seen by some observers as a long-shot but has been praised for a strong performance through the long campaign.
Voting was due to begin shortly after 3:00 pm (local time) but it may take several rounds and many hours to produce a winner, given WHO's complex voting system.
The organisation officially has 194 member-states, but only 186 nations were eligible to cast ballots Tuesday due to no-shows and voting rights stripped because of unpaid UN dues.
Previously the executive committee offered one candidate for states to rubber stamp.
WHO has already initiated a range of reforms since it faced crushing criticism for the Ebola crisis, but experts say the new chief still faces a huge task.
"We need WHO to be more effective than it is today," the director of Harvard University's Global Health Institute, Ashish Jha, said at the Swiss Press Club event.
He highlighted transparency and accountability especially for WHO leadership as areas that need work.
Mark Dybul, who heads the Global Fund To Fight AIDS, Tuberculosis and Malaria, said Chan had "laid the foundations" for improvements, but added that "big, big changes need to be made".
This was identified as a significant issue in the Ebola crisis, when the African office in Brazzaville was accused of not sounding the alarm.
The candidates made their final pitch to voters before the first ballots were cast.
Tedros, a malaria specialist, recalled the childhood death of his brother from a treatable sickness to underscore the importance of universal healthcare for all would be a top priority.
The 52-year-old said he refused "to accept that people should die because they are poor".
Nabarro, 67, reminded voters that he turned around the botched Ebola response when he was named UN special envoy for the crisis roughly a year into the outbreak.
Nishtar, 53 and the only female finalist, promised to embed "accountability and transparency" in the global health body.