The 21-year-old - who has already made two appearances for the senior national team - has made 66 league outings for Kosice, netting four times, since arriving from Kolubara Lazarevac in 2007.
He was set to star at this summer's U21 European Championships in Sweden, only for a broken metatarsal injury sustained in Serbia's opener against Italy to end his tournament prematurely.
However, the setback failed to quash speculation linking the youngster with a string of English sides - including Manchester United, Tottenham Hotspur, Aston Villa and Fulham, as well as Chelsea.
Matic said he was looking forward to joining up with fellow Serb Branislav Ivanovic at Stamford Bridge.
"I play with Branislav in the national team and have spoken to him about Chelsea," Matic, who had a trial with Middlesbrough last season, told Chelsea's website.
Chelsea said earlier on Tuesday that Peru striker Claudio Pizarro had joined Werder Bremen on a permanent basis after spending last season on loan at the Bundesliga club.
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