The rate and pathways of relaxation of a magnetic medium to its equilibrium following excitation with intense and short laser pulses are the key ingredients of ultrafast optical control of spins. Here we study experimentally the evolution of the magnetization and magnetic anisotropy of thin films of a ferromagnetic metal galfenol (Fe0.81Ga0.19) resulting from excitation with a femtosecond laser pulse. From the temporal evolution of the hysteresis loops we deduce that the magnetization MS and magnetic anisotropy parameters K recover within a nanosecond, and the ratio between K and MS satisfies the thermal equilibrium's power law in the whole time range spanning from a few picoseconds to 3 nanoseconds. We further use the experimentally obtained relaxation times of MS and K to analyze the laser-induced precession and demonstrate how they contribute to its frequency evolution at the nanosecond timescale.