Claessens and Vitesse had been at loggerheads ever since the club went back on their verbal agreement to let the player leave on a free transfer after a number of teams came forward and expressed interest.
The midfielder demanded that he be allowed to move on and the situation has been resolved before it turned ugly.
Genk and Lokeren were locked in a battle to sign Claessens, with the former winning the race after they agreed to end Janssen's loan spell at the club six months ahead of schedule.
The Belgian club signed Janssen (pictured) on a season-long loan deal from Vitesse in the summer but he failed to make an impression on coach Sef Vergoossen.
Genk have paid an undisclosed amount as well as handing back the services of Janssen in order to win the race for Claessens.
Claessens has signed a three-and-a-half-year deal with Genk.
