Two-dimensional (2D) materials such as graphene (Gr), molybdenum disulfide and hexagonal boron nitride (hBN) hold great promise for low-cost and ubiquitous electronics for flexible displays, solar cells or smart sensors. To implement this vision, scalable production, transfer and patterning technologies of 2D materials are needed. Recently, roll-to-roll (R2R) processing, a technique that is widely used in industry and known to be cost-effective and scalable, was applied to continuously grow and transfer graphene. However, more work is needed to understand the possibilities and limitations of this technology to make R2R processing of 2D materials feasible. In this work, we fabricated a custom R2R transferring system that allows accurate control of the process parameters. We employ continuous electrochemical delamination, known as “bubble transfer”, to eliminate chemical etchant waste and enable the continuous transfer of 2D materials from metal foils. This also makes our transfer method a renewable and environmental friendly process. We investigate the surface topology as well as the electrical parameters of roll-to-roll transferred graphene on polyethylene terephthalate (PET) coated with ethylene-vinyl acetate (EVA). Furthermore, we demonstrate for the first time the stacking of two layers of graphene or graphene on hBN by repeated lamination and delamination onto EVA/PET. These results are an important contribution to creating low-cost, large scale and flexible electronics based on 2D materials.