  We have discovered four X-ray bursts, recorded with the Rossi X-ray Timing
Explorer Proportional Counter Array between 2003 September and 2004 April, that
we show to originate from the transient magnetar candidate XTE J1810-197. The
burst morphologies consist of a short spike or multiple spikes lasting ~1 s
each followed by extended tails of emission where the pulsed flux from XTE
J1810-197 is significantly higher. The burst spikes are likely correlated with
the pulse maxima, having a chance probability of a random phase distribution of
0.4%. The burst spectra are best fit to a blackbody with temperatures 4-8 keV,
considerably harder than the persistent X-ray emission. During the X-ray tails
following these bursts, the temperature rapidly cools as the flux declines,
maintaining a constant emitting radius after the initial burst peak. During the
brightest X-ray tail, we detect a narrow emission line at 12.6 keV with an
equivalent width of 1.4 keV and a probability of chance occurrence less than 4
x 10^-6. The temporal and spectral characteristics of these bursts closely
resemble the bursts seen from 1E 1048.1-5937 and a subset of the bursts
detected from 1E 2259+586, thus establishing XTE J1810-197 as a magnetar
candidate. The bursts detected from these three objects are sufficiently
similar to one another, yet significantly different from those seen from soft
gamma repeaters, that they likely represent a new class of bursts from magnetar
candidates exclusive (thus far) to the anomalous X-ray pulsar-like sources.
