Markle, the duchess of Sussex, spoke to Obama, the former first lady of the United States, as the guest editor of the magazine's September issue.
Today confirmed the issue will feature a candid conversation between Markle, 37, and Obama, 55. It will also include an interview between Markle's husband, Prince Harry, and famed chimpanzee researcher Jane Goodall.
"These last seven months have been a rewarding process, curating and collaborating with Edward Enninful, British Vogue's editor-in-chief, to take the year's most read fashion issue and steer its focus to the values, causes and people making impact in the world today," Markle said in a statement.
"Through this lens I hope you'll feel the strength of the collective in the diverse selection of women chosen for the cover as well as the team of support I called upon within the issue to help bring this to light," she added. "I hope readers feel as inspired as I do, by the 'Forces of Change' they'll find within these pages."
Markle thanked Enninful, the featured women and her friends in an Instagram post Sunday.
"A huge thanks to all of the friends who supported me in this endeavor, lending their time and energy to help within these pages and on the cover. Thank you for saying 'Yes!' - and to Edward, thank you for this wonderful opportunity," she wrote.
Markle is the first guest editor of the September issue in British Vogue's 103-year history. The September issue is released online and on U.K. newsstands Friday.