We investigate the magnetic behavior of (Fe,Co) codoped ZnO both theoretically and experimentally. The electronic structure calculation for both bulk and cluster systems of codoped ZnO, within the framework of DFT+U, stabilizes in a ferrimagnetic configuration for nearest-neighbor position of the codopants. The exchange properties of the codoped system are dependent on the distance and concentration of the dopants. The theoretical calculations also reveal the importance of defect states in mediating the long-range magnetic order in such systems. Experimentally obtained magnetic properties for several ranges of doping suggest a competitive mixing of ferrimagnetic and ferromagnetic behaviors within the sample. The segregated phase for higher percentage of doping has also been identified.