The virtual meeting aims to raise $7.4 billion for immunisation programmes stalled by the pandemic, and will see the launch of a new fundraising drive to support potential COVID-19 vaccines.
"I hope this summit will be the moment when the world comes together to unite humanity in the fight against disease," Johnson said in a statement.
The British leader added he hoped it would "inaugurate a new era of global health co-operation, which I believe is now the most essential shared endeavour of our lifetimes".
More than 50 countries are taking part in Thursday's meeting, as well as individuals such as philanthropist Bill Gates, and will raise funds for Gavi, the vaccine alliance.
Over the next five years, it wants to reboot halted programmes and provide vaccines at a much-reduced cost to some 300 million children.
Gavi and its partners will also launch a financing drive to purchase potential COVID-19 vaccines, scale-up their production and support delivery to developing nations.
The pandemic has exposed new ruptures in international cooperation, notably with US President Donald Trump's decision to pull out of the World Health Organization (WHO).
But Johnson said helping developing countries would benefit places such as Britain, which has suffered the worst coronavirus death toll in Europe.
"This support for routine immunisations will shore up poorer countries' healthcare systems to deal with coronavirus -- and so help to stop the global spread," he told reporters on Wednesday.
"This virus has shown how connected we are. We're fighting an invisible enemy. And no one is safe frankly until we are all safe."