Type III solar radio bursts are the Sun's most intense and frequent nonthermal radio emissions. They involve two critical problems in astrophysics, plasma physics, and space physics: how collective processes produce nonthermal radiation and how magnetic reconnection occurs and changes magnetic energy into kinetic energy. Here magnetic reconnection events are identified definitively in Solar Dynamics Observatory UV-EUV data, with strong upward and downward pairs of jets, current sheets, and cusp-like geometries on top of time-varying magnetic loops, and strong outflows along pairs of open magnetic field lines. Type III bursts imaged by the Murchison Widefield Array and detected by the Learmonth radiospectrograph and STEREO B spacecraft are demonstrated to be in very good temporal and spatial coincidence with specific reconnection events and with bursts of X-rays detected by the RHESSI spacecraft. The reconnection sites are low, near heights of 5-10 Mm. These images and event timings provide the long-desired direct evidence that semi-relativistic electrons energized in magnetic reconnection regions produce type III radio bursts. Not all the observed reconnection events produce X-ray events or coronal or interplanetary type III bursts; thus different special conditions exist for electrons leaving reconnection regions to produce observable radio, EUV, UV, and X-ray bursts.