The former Pulp front man “leads us through some new thinking and creativity from when the world went quiet”, according to a statement from the publication.
The issue will feature an artwork by Jeremy Deller in its centrefold, as well as an interview with the artist.
Poet Caleb Femi, anthropologist David Graeber and broadcaster Emma Dabiri also feature in the magazine.
Cocker, 56, said: “This special edition of The Big Issue gives me the chance to present to you some of the humans who have excited or inspired me during the time of Covid, I would call them the heroes of our times.”
The issue also features a letter that Cocker would write to his younger self, which was partly inspired by his rediscovery of a school notebook.
Under the headline Pulp Masterplan, the musician reveals that he had written: “The group shall work its way into the public eye by producing fairly conventional, yet slightly offbeat, pop songs.
“After gaining a well-known and commercially successful status, the group can then begin to subvert and restructure both the music business and music itself.”
The Big Issue editor Paul McNamee said: “Jarvis remains one of Britain’s most creative and fascinating cultural voices, a man who, in a few lines, can effortlessly articulate state of the nation truths.
“It’s a joy to have him take over The Big Issue this week. It’s no surprise that his deep dive into what the lockdown meant for thinking and creativity spins off in arresting ways.
“We thank him for his time, his patience and his brilliant ideas.
“In a summer of flux and uncertainty, he has come up with something true to hold onto.”
Cocker’s edition of the magazine will be available from Monday.
