We report on the long term X-ray monitoring with Swift, RXTE, Suzaku, Chandra, and XMM-Newton of the outburst of the newly discovered magnetar Swift J1822.3–1606 (SGR 1822-1606), from the first observations soon after the detection of the short X-ray bursts which led to its discovery (July 2011), through the first stages of its outburst decay (April 2012). Our X-ray timing analysis finds the source rotating with a period of P = 8.43772016(2) s and a period derivative Ṗ = 8.3(2) × 10−14 ss−1, which entails an inferred dipolar surface magnetic field of B ≃ 2.7 × 1013 G at the equator. This measurement makes Swift J1822.3–1606 the second lowest magnetic field magnetar (after SGR 0418+5729; Rea et al. 2010). Following the flux and spectral evolution from the beginning of the outburst, we find that the flux decreased by about an order of magnitude, with a subtle softening of the spectrum, both typical of the outburst decay of magnetars. By modeling the secular thermal evolution of Swift J1822.3–1606, we find that the observed timing properties of the source, as well as its quiescent X-ray luminosity, can be reproduced if it was born with a poloidal and crustal toroidal fields of Bp ~ 1.5 × 1014 G and Btor ~ 7 × 1014 G, respectively, and if its current age is ~550 kyr (Rea et al. 2012).