This manuscript describes the development and operation of an apparatus for the measurement of steady-state and transient gas permeation through different types of solid materials with varying geometries. It is capable of operation from 293 K to 673 K and could theoretically be used with any non-corrosive gas or a mix of gases, although only hydrogen isotopes are used in the current study. A quadrupole mass spectrometer is used to measure permeation fluxes as low as 1011 molecules/s. This unique test setup allows for the simultaneous measurement of diffusivity, solubility, and permeability. Furthermore, varying the pressure in the fore-sample volume allows for tests of Sievert's law and can give information on surface effects.