Alcott, who finished 11th at the last two Winter Olympics, is self-funded and as a result trains with other national teams, as it is significantly cheaper to contribute to one share of an overall funding project than to train alone.
She has trained with Canada in the past but will now link up with Norway head coach Stefan Abplanalp, who she has worked with for much of her career.
"I would never ever leave my country, this is just the strange situation to get there," Alcott told the BBC while explaining that she would continue to represent Great Britain.
Despite being the only genuinely world-class skier in Britain, Alcott lost her funding in 2010 after UK Sport withdrew financial support for alpine skiing in the build-up to the Sochi Games.
The 30-year-old, who now supports herself through sponsorship deals, then suffered a badly broken leg that ruled her out of the entire 2011-12 season.
But she has returned to action with a degree of success and is hoping to finish in the top eight in Sochi.
"I used to get really bitter and it used to make me really sad that I was ranked eighth in the world and not getting any money from UK Sport but I've got used to it now," Alcott said.
"This is my last Olympics and it could be my last season skiing. I've got a lot to prove and I don't want to waste any energy on fighting the system anymore.
"So I'm just going out there with my head down and my focus on achieving my best result ever at Sochi. That's the aim and always has been."
Britain has a limited pool of skiing talent, with most of its wintersports success coming in ice sports like curling, bobsleigh and skeleton.
Alcott is something of an anomaly in that she is widely regarded to have been one of the top-10 alpine skiers in recent years, but UK Sport's strict funding rules make her relative personal success irrelevant if her team-mates fail to place at international events.