Despite original plans for an "earthy" outdoor fall wedding at home, the "Catch My Breath" singer, 31, revealed to PEOPLE on Wednesday, "We are so busy that we finally just came to terms the other night and were like, 'So, we change our minds and we want to elope.' We just got so overwhelmed by it – all the decisions."
Explains Clarkson: "We sent out a save-the-date to everyone and then it got crazy and all the details were leaking."
"Then honestly the planning – I have a Christmas record coming out. I'm doing a bunch of stuff with State Farm right now (the singer is teaming up with the insurance company to educate kids about safe driving). We have two kids who just started school. We're going to all these football games and soccer games and volleyball games and [Brandon]'s got one of the biggest artists [Blake Shelton] in country music. He's flying everywhere."
When the musically inclined pair finally made their decision about how to say "I do," they "sent out an engagement photo to everyone and said, 'Thank you so much for understanding, but it's just going to be me and Brandon and his two kids and the minister,' " Clarkson says.
And even after they elope, an extravagant fête is the furthest thing from their minds.
"Our whole life is a celebration," the former American Idol winner says. "That's what we kept laughing about. We don't need another day where we throw a big party. Our lives are so in the spotlight all the time. Everything is such a spectacle, we were like, 'We would rather have an intimate moment that's special.' "
But that doesn't mean their lives will be soirée-free.
"We're going to do that anyway," she says. "Our friend is throwing us [a party] because we're about to wrap up construction at our house. He's throwing us a huge stock the bar party, so all of the people who were going to be at our wedding will be there."
How Their Love Story Inspired Her New VideoBig wedding or small, the idea of walking down the aisle seems to be on Clarkson's mind.
In the new music video for her song, "Tie It Up," several happy couples wed while Clarkson rocks out onstage and belts out lyrics like, "Let's set the date/let's hire the band/let's cut the cake/tie up the cans ... "
The singer proudly shows off her own engagement ring in the video and can be seen wearing a white dress – though it's not clear if it's a wedding dress. But one thing is obvious: Clarkson appears to be very excited about tying the knot herself – so excited that the video ends with her catching the bouquet!
Of the video, she explains, "One of my really good friends was with me when I first met Brandon years ago, so she and another one of my friends wrote this cool song that deals with our whole story, so we went to this really beautiful barn in Franklin, Tenn., and all of the people in the video are friends or friends of friends. We were like, 'We're going to have this fake wedding reception.' "
See the video for "Tie It Up" below: