Davies struggled to find playing time at Sochaux after returning from injuries sustained in an October 2009 car crash, and spent last year on loan with Major League Soccer's D.C. United. After the crash, he made just two appearances for the French club, both as a second-half substitute in February.
Davies said on Randers' website that the deal ''gives me a great chance to show I can be a success on European soil.''
Randers club director Jacob Nielsen said the 26-year-old American will bring more speed to the lineup and that ''he will fit in well with our current team of attackers.''
Davies had become a starter on the U.S. national team before the car accident, which nearly took his life.
He was set to take part in his first training session with Randers on Saturday.