The Dynamo Kiev star had generated interest in Italy while Red Star Belgrade were also reported to be considering a move.
However Evian, 17th in Ligue 1 - one place and three points outside the relegation zone - have secured his services.
Ninkovic, 28, has 28 caps for his country and has played in Ukraine for Dynamo since 2004. His contract runs out this year.
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- Red Star Belgrade