Editor Edward Enninful said the issue is a "rallying cry for the future" and includes 40 activists described as "The Faces of Hope".
The September issue is traditionally the fashion bible's most important of the year. The Duchess of Sussex guest edited the issue 12 months ago.
Premier League star Rashford was praised earlier this year for leading a campaign against child poverty while Aboah is a mental health campaigner.
Introducing British Vogue’s September 2020 issue, starring 20 inspirational activists dedicated to making a change. With @MarcusRashford and @Adwoaaboah_ photographed by @misanharriman, leading on the special fold-out cover: https://t.co/7rbRA0iXAS pic.twitter.com/CEhRRXN7yF— British Vogue (@BritishVogue)August 3, 2020
They were photographed by Misan Harriman, the first black male photographer to shoot a British Vogue cover in its 104-year history, with a predominantly black team on set.
Among the activists to feature in the September issue are Radio 1 DJ Clara Amfo, racial justice campaigner Baroness Doreen Lawrence, model Joan Smalls, author Reni Eddo-Lodge, Black Lives Matter co-founder Patrisse Cullors and writer Janet Mock.
Rashford, 22, said: "I'm by no means a politician but I had a voice and a platform that could be used to at least ask the questions.
"If I didn't put myself out there and say, 'This is not OK and it needs to change,' I would have failed my 10-year-old self."
Aboah, 28, said: "For some time it's felt to me to have been quite a box-ticking approach to racial justice, mental health, sustainability. Now I have hope it's changing. I don't think you're going to get away with just spraying perfume on the situation anymore."
Vogue's Hope issue is a collaboration between all 26 editions of the magazine around the world for the September and October issues.
It marks the first time in Vogue's 128-year history that all editions are consolidating under a singular editorial theme.
The September issue of British Vogue will be available on newsstands and digital download on Friday August 7.