Given an Orlicz function H satisfying the \Delta_2 property at zero, one can use the Orlicz sequence space \mathcal l_H to define a tensor norm g^c_H and the minimal ( H^c -nuclear) and maximal ( H^c -integral) operator ideals associated to g^c_H in the sense of Defant and Floret. The aim of this paper is to characterize H^c -integral operators by a factorization theorem.