The 28-year-old Neustadter was born in Ukraine but has lived in Germany since he was a child and played for Germany's youth teams.
On May 25, Neustadter was granted a Russian passport and he played for Russia at the European Championship in France, where he won two caps.
He played 30 times for Schalke 04 in the Bundesliga last season before his contract expired.
Fenerbahсe finished second in the Turkish championship last season and will play in the third qualifying round of the Champions League.
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(Reporting By Dmitriy Rogovitskiy; Editing by Clare Fallon)
