SGR 1833-0832 was discovered on 2010 March 19 thanks to the Swift detection of a short hard X-ray burst and follow-up X-ray observations. Since then, it was repeatedly observed with Swift, Rossi X-ray Timing Explorer, and XMM-Newton. Using these data, which span about 225 days, we studied the long-term spectral and timing characteristics of SGR 1833-0832. We found evidence for diffuse emission surrounding SGR 1833-0832, which is most likely a halo produced by the scattering of the point source X-ray radiation by dust along the line of sight, and we show that the source X-ray spectrum is well described by an absorbed blackbody, with temperature kT=1.2 keV and absorbing column nH=(10.4+/-0.2)E22 cm^-2, while different or more complex models are disfavoured. The source persistent X-ray emission remained fairly constant at about 3.7E-12 erg/cm^2/s for the first 20 days after the onset of the bursting episode, then it faded by a factor 40 in the subsequent 140 days, following a power-law trend with index alpha=-0.5. We obtained a phase-coherent timing solution with the longest baseline (225 days) to date for this source which, besides period P=7.5654084(4) s and period derivative dP/dt=3.5(3)E-12 s/s, includes higher order period derivatives. We also report on our search of the counterpart to the SGR at radio frequencies using the Australia Telescope Compact Array and the Parkes radio telescope. No evidence for radio emission was found, down to flux densities of 0.9 mJy (at 1.5 GHz) and 0.09 mJy (at 1.4 GHz) for the continuum and pulsed emissions, respectively, consistently with other observations at different epochs.
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