New WHO head Dr Tedros Adhanom Ghebreyesus praised Zimbabwe for its commitment to public health.
But critics say that during Mr Mugabe's 37-year rule Zimbabwe's health services have deteriorated, with staff regularly unpaid and medicines in short supply.
Dr Tedros, who is Ethiopian, is the first African to lead the WHO.
He was elected with a mandate to tackle perceived politicisation in the organisation.
Dr Tedros replaced Margaret Chan, who stepped down from her 10-year post in June.
The BBC's Geneva correspondent Imogen Foulkes said the appointment of Robert Mugabe, 93, would cause astonishment among many WHO member states and donors.
A goodwill ambassador may be a largely symbolic role, but the symbolism of giving it to a man whose leadership of Zimbabwe has, critics say, coincided with a collapse of its health service, and major human rights abuses, will be very unpopular, she said.
Photo: AFP Critics say health services in Zimbabwe have deteriorated during President Robert Mugabe's rule.