The 25-year-old model from Russia was unveiled as the publication's latest cover girl during Monday night's episode of Late Night With David Letterman.
"We Russians know all the secrets but I didn't know I would land the cover!" she told Matt Lauer and Meredith Vieira on NBC's Today Show this morning. "It was a total surprise for me and I was in shock. I was crying!"
She added: "It's a dream come true."
As for the future, the model - who declined to talk about boyfriend Cristiano Ronaldo - said that she just wanted to "enjoy this moment" because the news was still sinking in.
Shayk had appeared on Letterman alongside nine other models for the unveiling of the magazine's cover on a giant billboard in Times Square. Her cover was shot in Hawaii by photographer Bjorn Iooss.
The swimsuit edition is available now.