Enninful said he was "so excited" walking into Kensington Palace, to which Meghan replied: "Oh my gosh."
Enninful continues: "I was like, 'Lovely to meet you, Duchess.' And you were like... 'Call me Meghan!'"
After Enninful agreed to work with her on the Smart Works charity project, Meghan explained that she asked him if he would be willing to let her guest edit an edition of Vogue.
Meghan admitted that she left the fashion element "to the professionals", but did add: "I did say, 'Can you do Commonwealth fashion?' 'Can you do sustainability?' 'Can we make sure the point of view is really in the right ethos?' And then I'll leave it to the experts."
Enninful replied: "You wanted to focus on women who are changing the world, women who are doing incredible things, which really is in line with what we do at British Vogue."
Meghan went on to reveal she had a "surprise" for Enninful, to congratulate him for bringing her vision to life.
She handed the editor a glittery hat and put on a small silver one herself and the duo blew party horns before sharing a laugh.