كتب : Sherif Tarek
The London side didn't reveal the transfer fee; however, BBC reported that the deal went through for ₤1,5 million.
The up-and-coming youngster, who should get back from injury in November, joined the Blues from Slovakian side MFK Kosice on a four-year deal.
Now Matic is hoping to secure a regular place at Stamford Bridge.
"I know a lot about Chelsea, I have been following them," Matic, 21, told the club's official website.
"I play together with Branislav (Ivanovic) in the national team and have spoken to him about Chelsea. The first time I met him to play in the national team I asked a couple of questions.
"I am a solid midfield player, I have a lot to offer and for sure to progress and I will show everyone why I am at Chelsea.
"I am a central midfielder, and I know I am not well known but I have physical power and I am a quite technical, left-footed player.
"Since the age of 18 I have been at Kosice and before that I had played in the youth team of Red Star Belgrade."