Boss Tony Mowbray said: "Having offered Zoltan the best contract the club could at this time, we could do no more. "We would like to wish Zoltan all the best in his future career.
"Everyone at Albion appreciated his professionalism on and off the field.
"But football moves on and, just as we did last summer, we are looking forward to the challenge of finding new faces to strengthen the squad for the season ahead."
His ten goals from midfield in all competitions last term helped Mowbray's men clinch promotion back to the Barclays Premiership as Coca-Cola Championship champions and reach the FA Cup semi-finals.