The French first division side announced the transfer on Thursday. The 23-year-old striker, scorer of 22 goals for tHammarby, is the first ever American to play for the French club.
Davies was spotted while playing for low-profile side Westchester Flames and went to Holland for a trial with Ajax. He then joined the Swedish club in January 2007.
He has played for the USA team on thirteen occasions, scoring four times.
The striker will be expected to fill the Sochaux forward spot vacated by Turkey international Mevlut Erding who transferred last month to Paris St Germain.