The Swiss-born 20-year-old defensive midfielder, who joined Tottenham in 2011 but failed to break through to the senior squad, had spent the past season on loan at Middlesbrough and Charlton Athletic, making only sporadic appearances.
He won the Under-20 world cup last year with Serbia.
"We had Milos on our screens for a long time and we are happy to have brought him here," said Werder sports director Thomas Eichin. "This transfer is an investment for the future."
Werder are struggling this season and are in the relegation playoff spot, on 19 points.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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