We present a reliable technique for irreversibly bonding chemically inert Viton® membranes to PMMA and COC substrates to produce microfluidic devices with integrated elastomeric structures. Viton® is widely used in commercially available valves and has several advantages when compared to other elastomeric membranes currently utilised in microfluidic valves (e.g. PDMS), such as high solvent resistance, low porosity and high temperature tolerance. The bond strength was sufficient to withstand a fluid pressure of 400 kPa (PMMA/Viton®) and 310 kPa (COC/Viton®) before leakage or burst failure, which is sufficient for most microfluidic applications. We demonstrate and characterise on-chip pneumatic Viton® microvalves on PMMA and COC substrates. We also provide a detailed method for bonding fluorinated Viton® elastomer, a highly chemically compatible material, to PMMA and COC polymers. This allows the production of microfluidic devices able to handle a wide range of chemically harsh fluids and broadens the scope of the microfluidic platform concept.