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."
The event will be recorded on Sunday at the SoFi Stadium in Los Angeles, and broadcast on 8 May.
Vax Live is calling on governments to commit to vaccine equity by donating doses and resources.
The campaign is also pushing businesses to "donate dollars for doses", and for pharmaceutical companies to make vaccines available at not-for-profit prices.
In their role as campaign chairs, Harry and Meghan have been encouraging the private sector to make donations to the Covax scheme, which is co-led by the World Health Organization (WHO) and aims to ensure vaccines are shared fairly among all nations, rich and poor.
More than one billion doses of coronavirus vaccines have now been administered worldwide. But there are vast differences in the pace of progress in different parts of the world, with some countries having delivered doses to a large proportion of their population and others still waiting for their first shipments to arrive.
The concert will feature performances from artists including Jennifer Lopez, Foo Fighters and Pearl Jam's Eddie Vedder.
Mr Biden, his wife Jill and Vice-President Kamala Harris will promote the "We Can Do This" initiative, which seeks to increase confidence in Covid-19 vaccines
French President Emmanuel Macron, Canadian Prime Minister Justin Trudeau, and Croatian Prime Minister Andrej Plenkovic will also make appearances.
Last year, Global Citizen partnered with the WHO to put on a virtual concert to celebrate healthcare workers.