New Twente boss McClaren was delighted to have beaten off competition from several clubs to land Rajkovic.
The former England manager told the club's official website: "I am pleased that we could add such a young player with all his qualities to our squad.
"When we got the opportunity to add him to our group we immediately did so.
"Many clubs, especially in England, wanted his signature. I want to have as strong a squad as possible with competition for places in each position. And he can play in several positions in defence."