Let \(R\) be a commutative Noetherian ring with identity, \(I,J\) two ideals of \(R\) and \(M\) an \(R\)-module. The notion of the generalized local cohomology modules \(\text{H}^{i}_{I,J}(M)\) was introduced by \textit{R. Takahashi} et al. [J. Pure Appl. Algebra 213, No. 4, 582--600 (2009; Zbl 1160.13013)]. Let \[ \widetilde{W}(I,J):=\left\{\mathfrak{a} R\;|\;I^{n} \subseteq \mathfrak{a}+J\text{ for some } n\geq 1\right\}. \] The endofunctor \(\Gamma_{I,J}(-)\) on the category of \(R\)-modules is defined by setting \[ \Gamma_{I,J}(M):= \left\{x\in M \;|\;\mathrm{Supp}_{R}(Rx) \subseteq (\widetilde{W}(I,J)\cap \text{Spec} R) \right\}, \] and \(\Gamma_{I,J}(f):= f|_{\Gamma_{I,J}(M)}\) for an \(R\)-homomorphism \(f:M\rightarrow N\). For each integer \(i\geq 0\), the \(i\)th local cohomology functor with respect to the pair \((I,J)\) is defined to be \(\text{H}^{i}_{I,J}(-): =R^{i}\Gamma_{I,J}(-)\). In this paper, the authors introduce the notion of the ideal transform functor with respect to the pair \((I,J)\) by \[ D_{I,J}(-):=\underset {\mathfrak{a}\in \widetilde{W}(I,J)}{\varinjlim}D_{\mathfrak{a}}(-). \] This notion is a generalization of the usual ideal transform functor, that corresponds to the case \(J=0\). The authors extend many results concerting usual local cohomology and ideal transform functors to the corresponding statements for the functors \(\text{H}^{i}_{I,J}(-)\) and \(D_{I,J}(-)\). In particular, the show that the functor \(D_{I,J}(-)\) is exact if and only if \(\text{H}^{i}_{I,J}(N)=0\) for all \(i\geq 2\) and for all finitely generated \(R\)-modules \(N\).