The 'I Want it That Way' singer popped the question to Kitt while the couple were on holiday in the Florida Keys, according to People.
"I had the ring in my pocket for two weeks… I was like, 'I don't want it anymore'," Carter recalled of the proposal.
"It was driving me insane. I just wanted to get it out of my hands and on to hers."
Carter then joked that he was actually surprised that Kitt accepted his proposal, saying: "She said, 'Yes', and I'm, like, 'I don't know what to do'.
"[Lauren] said, 'You're supposed to put it on my finger'. So I did. I was in shock'."
Kitt added: "I wasn't expecting it. It just felt very surreal. We both are just so happy in love right now and on cloud nine."
Carter's engagement comes amid happy developments in the lives of two of his Backstreet Boys bandmates.
Howie Dorough and AJ McLean have both welcomed babies with their respective spouses.
Watch Backstreet Boys' 'Quit Playing Games (with My Heart)' music video below: