Gilbert damping and saturation magnetization are of critical importance for magnetic thin films in spintronic devices. Using complementary techniques, including ferromagnetic resonance (FMR), superconducting quantum interference device (SQUID) measurements, and energy dispersive x-ray spectroscopy, we demonstrate that Gilbert damping and magnetization in Fe1????B?? thin films can be tuned by controlling the B concentration ??. At low B concentration, FMR and SQUID measurements show a strong reduction of the magnetic damping and the saturation magnetization, respectively. A very low magnetic damping of around 3.8×10?3 is measured at ??=25%, which is among the lowest damping values reported so far for a conducting ferromagnet. This tunability of magnetic properties will be useful for fabricating thin films with low damping that can be used in high-performance spintronic devices.