Britain called the decision "surprising and disappointing, particularly in light of the current United States and European Union sanctions against him".
"I thank everyone who has voiced their concerns and shared their thoughts".
"Mugabe doesn't trust Zimbabwe health care he destroyed (he travels abroad) but @WHO's Tedros names him ambassador", the head of Human Rights Watch, Ken Roth, added in a tweet.
Speaking at a conference in Uruguay, Ghebreyesus described Zimbabwe as "a country that places universal health coverage and health promotion at the centre of its policies to provide healthcare to all" and said Mugabe could "influence his peers in his region".
Mugabe, who has been in power since 1980, is in increasingly fragile health and makes regular trips overseas for medical treatment.
"The only person whose health 93-yo Mugabe has looked out for in his 37 year reign is his own".
"The government of Robert Mugabe presided over the dramatic reversal of its population's access to food, clean water, basic sanitation and health care", the physicians said, adding that the result was "the shuttering of hospitals and clinics, the closing of its medical school and the beatings of health workers".
His election as the first African leader of World Health Organization was billed as a key moment for the continent, where much of organisation's work is based. "The notion that the United Nations should now spin this country as a great supporter of health is, frankly, sickening".
Outside Zimbabwe, many World Health Organization member-states and rights groups criticised Mugabe's appointment.
The Director-general of WHO said he had "listened carefully" to the criticism and felt the decision is in the best interests of the World Health Organisation.
"Zimbabwe's government has not commented on Mugabe's appointment, but a state-run Zimbabwe Herald newspaper headline called it a "new feather" in the president's cap".
Salani Mutseyami, a spokeswoman for the campaign groups Zimbabwe Vigil and Restoration of Human Rights, told the Daily Telegraph: "That is absolutely absurd".
Twenty-six health bodies from around the world, including the World Heart Federation, Action Against Smoking and Cancer Research UK, released a joint statement condemning Mugabe's new role.