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van der Waals (vdW) heterostructures, stacking different two-dimensional materials, have opened up unprecedented opportunities to explore new physics and device concepts. Especially interesting are recently discovered two-dimensional magnetic vdW materials, providing new paradigms for spintronic applications. Here, using density functional theory (DFT) calculations, we investigate the spin-dependent electronic transport across vdW magnetic tunnel junctions (MTJs) composed of Fe 3 GeTe 2 ferromagnetic electrodes and a graphene or hexagonal boron nitride ( h -BN) spacer layer. For both types of junctions, we find that the junction resistance changes by thousands of percent when the magnetization of the electrodes is switched from parallel to antiparallel. Such a giant tunneling magnetoresistance (TMR) effect is driven by dissimilar electronic structure of the two spin-conducting channels in Fe 3 GeTe 2 , resulting in a mismatch between the incoming and outgoing Bloch states in the electrodes and thus suppressed transmission for an antiparallel-aligned MTJ. The vdW bonding between electrodes and a spacer layer makes this result virtually independent of the type of the spacer layer, making the predicted giant TMR effect robust with respect to strain, interface distance, and other parameters, which may vary in the experiment. We hope that our results will further stimulate experimental studies of vdW MTJs and pave the way for their applications in spintronics.