A huge amount of thermal energy is available close to material surfaces in radiative and non-radiative states, which can be useful for matter characterization or for energy devices. One way to harness this near-field energy is to scatter it to the far field. Another way is to bring absorbers close to thermal emitters, and the advent of a full class of novel photonic devices exploiting thermal photons in the near field has been predicted in the last two decades. However, efficient heat-to-electricity conversion of near-field thermal photons, i.e. the seminal building block, could not be achieved experimentally until now. Here, by approaching a micron-sized infrared photovoltaic cell at nanometric distances from a hot surface, we demonstrate conversion efficiency up to 14% leading to unprecedented electrical power density output (7500 W.m-2), orders of magnitude larger than all previous attempts. This proof of principle is achieved by using hot graphite microsphere emitters (~800 K) and indium antimonide cells, whose low bandgap energy matches the emitter infrared spectrum and which are specially designed for the near field. These results pave the way for efficient photoelectric detectors converting thermal photons directly in the near field. They also highlight that near-field thermophotovoltaic converters, which harvest radiative thermal energy in a contactless manner, are now competing with other energy-harvesting devices, such as thermoelectrics, over a large range of heat source temperatures.