"As a musician, you have fantasies that you want to win Grammys, but I didn't really think that this was on the table," the singer tells PEOPLE in this week's cover story. "I was just amazed and stunned and it almost seemed like they were kidding, but they weren't, so that's cool."
The L.A.-raised Levine also reveals that he cries at movies (E.T. The Extra-Terrestrial always gets him), loves to be naked and is looking forward to settling down with his fiancée, Victoria's Secret model Behati Prinsloo. "I didn't think marriage was for me for a long time," the 34-year-old says. "I was ready when I was ready. That's about as simple as it could possibly be."
As for that incredible body, Levine credits yoga and spinning for keeping his stamina up, especially as his success continues to skyrocket. "This is just a really interesting time where everything seems to be heading in a certain direction," he adds. "And I'm not taking any of it for granted."
For more of our exclusive interview and photo shoot with Levine, including what he finds most attractive in women and his thoughts on becoming a dad, pick up this week's issue of PEOPLE on newsstands Friday