We present a compact and robust setup to optically transport ultracold atoms over long distances. Using a focus-tunable moiré lens that has recently appeared in the market, we demonstrate transport of up to a distance of 465 mm. A transfer efficiency of 70% is achieved with a negligible temperature change at 11 μK. With its high thermal stability and low astigmatism, the moiré lens is superior to fluid-based varifocal lenses. It is much more compact and stable than a lens mounted on a linear translation stage, allowing for simplified experimental setups.