"I feel humbled and honoured to be elected," said Robinson, who added that GAVI had achieved "extraordinary success through its unique public and private approach to improving the health of the world's poor."
Established by IT magnate Bill Gates and funded by donor governments, international institutions and private philanthropists, the GAVI alliance runs vaccination programmes against diseases such as meningitis and tuberculosis in the world's poorest countries.
Robinson will head a 28-member executive board including representatives from developing countries, donor governments, UNICEF, the World Health Organisation and the World Bank as well as private institutions.
"The new board structure embodies this approach and will enable us to meet the challenges ahead," Robinson said.
GAVI said Wednesday that its immunisation programmes against meningitis and hepatitis will have averted 3.4 million deaths by the end of the year.