We demonstrate efficient nanowire superconducting single photon detectors (SSPDs) based on NbN thin films grown on GaAs. NbN films ranging from 3 to 5 nm in thickness have been deposited by dc magnetron sputtering on GaAs substrates at 350 degrees C. These films show superconducting properties comparable to similar films grown on sapphire and MgO. In order to demonstrate the potential for monolithic integration, SSPDs were fabricated and measured on GaAs/AlAs Bragg mirrors, showing a clear cavity enhancement, with a peak quantum efficiency of 18.3% at lambda=1300 nm and T=4.2 K. (C) 2010 American Institute of Physics. [doi:10.1063/1.3496457]