We report the discovery of a new X-ray pulsar, XTE J1810 - 197, that was serendipitously discovered on 2003 July 15 by the Rossi X-Ray Timing Explorer (RXTE) while observing the soft gamma repeater SGR 1806 - 20. The pulsar has a 5.54 s spin period, a soft X-ray spectrum ( with a photon index of approximate to 4), and is detectable in earlier RXTE observations back to 2003 January but not before. These show that a transient outburst began between 2002 November 17 and 2003 January 23 and that the source's persistent X-ray flux has been declining since then. The pulsar exhibits a high spin-down rate (P) over dot approximate to 10(-11) s s(-1) with no evidence of Doppler shifts due to a binary companion. The rapid spin-down rate and slow spin period imply a supercritical characteristic magnetic field B similar or equal to 3 x 10(14) G and a young age tau less than or equal to 7600 yr. Follow-up Chandra observations provided an accurate position of the source. Within its error radius, the 1.5 m Russian-Turkish Optical Telescope found a limiting magnitude R-C = 21.5. All such properties are strikingly similar to those of anomalous X-ray pulsars and soft gamma repeaters, providing strong evidence that the source is a new magnetar. However, archival ASCA and ROSAT observations found the source nearly 2 orders of magnitude fainter. This transient behavior and the observed long-term flux variability of the source in absence of an observed SGR-like burst activity make it the first confirmed transient magnetar and suggest that other neutron stars that share the properties of XTE J1810 - 197 during its inactive phase may be unidentified transient magnetars awaiting detection via a similar activity. This implies a larger population of magnetars than previously surmised and a possible evolutionary connection between magnetars and other neutron star families.