Electrolysis followed by underground hydrogen storage (UHS) in both salt caverns and depleted oil and gas reservoirs is widely considered as a potential option to overcome fluctuations in energy provision from intermittent renewable sources. Particularly in the case of depleted oil and gas reservoirs, a denser layer of cushion gas (N₂, CH₄ or CO₂) can be accommodated in these storage volumes to allow for sufficient system pressure control as hydrogen is periodically injected and extracted. These gases/fluids are however fully soluble with hydrogen and thus with sufficient mixing can undesirably contaminate the extracted hydrogen product. Fluid mixing in a porous medium is typically characterized by a dispersion coefficient (K_L), which is hence a critical input parameter into reservoir simulations of underground hydrogen storage. Such dispersion data is however not readily available in the literature for hydrogen at relevant storage conditions. Here we have developed and demonstrated novel methodology for the measurement of K_L between hydrogen and nitrogen in a Berea sandstone at 50 bar as a function of displacement velocity (0.007–0.722 mm/s). This leverages off previous work quantifying K_L between carbon dioxide and methane in rock cores relevant to enhanced gas recovery (EGR). This used infrared (IR) spectroscopy to differentiate the two fluids, hydrogen is however IR invisible. Hence the required time-resolved quantification of hydrogen concentration emerging from the rock core is uniquely performed here using bench-top nuclear magnetic resonance (NMR). The resultant hydrogen-nitrogen dispersion data as a function of displacement velocity allows for the determination of dispersivity (α = 0.31 mm). This intrinsic rock property compares favorably with previous CO₂ dispersion measurements on similar sandstones, hence validating our methodology to some extent. In addition, at very low velocities, determination of the rock core tortuosity (τ, another intrinsic rock property) produces a value (τ = 10.9) that is similar to that measurement independently using pulsed field gradient NMR methods (τ = 11.3).