The couple were announced as campaign chairs of the Vax Live event, organised by anti-poverty group Global Citizen.
US President Joe Biden will also appear at the concert, which is being hosted by pop star Selena Gomez.
"We will all benefit, we will all be safer, when everyone, everywhere has equal access to the vaccine," Harry and Meghan said.
"We must pursue equitable vaccine distribution and, in that, restore faith in our common humanity. The mission couldn't be more critical or important."