The 27-year-old makes the move to the Stade Saint-Symphorien just over three years after joining United from Monaco.
During his time on Tyneside, the French forward also spent time out on loan at Spanish side Osasuna, where he spent the entirety of last season.
Since his arrival in the summer of 2014, Rivière made 31 appearances in all competitions for the Magpies, scoring three goals.