Magnetic-field reconnection is believed to play a fundamental role in magnetized plasma systems throughout the Universe1, including planetary magnetospheres, magnetars and accretion disks around black holes. This letter present extreme ultraviolet and X-ray observations of a solar flare showing magnetic reconnection with a level of clarity not previously achieved. The multi-wavelength extreme ultraviolet observations from SDO/AIA show inflowing cool loops and newly formed, outflowing hot loops, as predicted. RHESSI X-ray spectra and images simultaneously show the appearance of plasma heated to >10 MK at the expected locations. These two data sets provide solid visual evidence of magnetic reconnection producing a solar flare, validating the basic physical mechanism of popular flare models. However, new features are also observed that need to be included in reconnection and flare studies, such as three-dimensional non-uniform, non-steady and asymmetric evolution. ; Comment: This is the accepted version. The paper was published in Nature Physics (2013)