This Letter demonstrates the transporting and focusing of laser-accelerated 14 MeV protons by permanent magnet miniature quadrupole lenses providing field gradients of up to 500 T/m. The approach is highly reproducible and predictable, leading to a focal spot of (286 x 173) microm full width at half maximum 50 cm behind the source. It decouples the relativistic laser-proton acceleration from the beam transport, paving the way to optimize both separately. The collimation and the subsequent energy selection obtained are perfectly applicable for upcoming high-energy, high-repetition rate laser systems.