The 20-year-old will move to Russia on a season-long loan deal.
Out of favour at Premier League side Everton, Vlasic has been forced to say "goodbye" to Merseyside and will compete in the Russian League this season.
'Toffees' boss Marco Silva has not expressed any intention of keeping Vlasic in his plans.
Middlesbrough came in with a Deadline Day bid for the midfielder, though Everton reportedly rejected the offer.