A fee was agreed for the Italy international on Friday, and he has now agreed personal terms.
Rossi will be officially presented to the media on Monday, but will not get the chance to play for his new club for another couple of months as he is currently sidelined with a serious knee injury.
The 25-year-old suffered cruciate ligament damage in October 2011 and has had to have surgery three times in the past 18 months.
Rossi started his professional career with Manchester United and also had loan spells with Newcastle United and Parma before joining Villarreal in 2007.
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