  Swift J1822.3-1606 was discovered on 2011 July 14 by the Swift Burst Alert
Telescope following the detection of several bursts. The source was found to
have a period of 8.4377 s and was identified as a magnetar. Here we present a
phase-connected timing analysis and the evolution of the flux and spectral
properties using RXTE, Swift, and Chandra observations. We measure a spin
frequency of 0.1185154343(8) s$^{-1}$ and a frequency derivative of
$-4.3\pm0.3\times10^{-15}$ at MJD 55761.0, in a timing analysis that include
significant non-zero second and third frequency derivatives that we attribute
to timing noise. This corresponds to an estimated spin-down inferred dipole
magnetic field of $B\sim5\times10^{13}$ G, consistent with previous estimates
though still possibly affected by unmodelled noise. We find that the
post-outburst 1--10 keV flux evolution can be characterized by a
double-exponential decay with decay timescales of $15.5\pm0.5$ and $177\pm14$
days. We also fit the light curve with a crustal cooling model which suggests
that the cooling results from heat injection into the outer crust. We find that
the hardness-flux correlation observed in magnetar outbursts also characterizes
the outburst of Swift J1822.3-1606. We compare the properties of Swift
J1822.3-1606 with those of other magnetars and their outbursts.
