The 21-year-old British singer is fleeing the UK to marry The Cribs frontman Ryan Jarman in a private US ceremony on Saturday.
A source told Britain's The Sun newspaper: "They are both very excited about the wedding but they didn't want any fuss. That's part of the reason why they decided to do it in America."
The pop pair who announced they were dating in September 2007 after meeting on British music TV show Later. With Jools Holland will say their vows in front of close family and friends in Portland, Oregon.
Nash - who shot to fame following the phenomenal success of her debut album Made of Bricks was reluctant to have a big wedding because she dislikes being in the showbiz spotlight.
She previously said: "I can't knock it really - I've chosen to be a musician because I love it. But I feel really uncomfortable with the whole showbiz party thing. It's just not my scene and it can be intimidating.
"I'll be in a room full of people name-dropping and schmoozing and I think, 'This is doing my head in.' I feel embarrassed when people are impressed by it all, especially when they're older than me. It's easy to get sucked in."