  We compute the sensitivity to dark matter annihilations for the forthcoming
large Cherenkov Telescope Array (CTA) in several primary channels and over a
range of dark matter masses from 30 GeV up to 80 TeV. For all channels, we
include inverse Compton scattering of e$^\pm$ by dark matter annihilations on
the ambient photon background, which yields substantial contributions to the
overall gamma-ray flux. We improve the analysis over previous work by: i)
implementing a spectral and morphological analysis of the gamma-ray emission;
ii) taking into account the most up-to-date cosmic ray background obtained from
a full CTA Monte Carlo simulation and a description of the diffuse
astrophysical emission; and iii) including the systematic uncertainties in the
rich observational CTA datasets. We find that our spectral and morphological
analysis improves the CTA sensitivity by roughly a factor 2. For the hadronic
channels, CTA will be able to probe thermal dark matter candidates over a broad
range of masses if the systematic uncertainties in the datasets will be
controlled better than the percent level. For the leptonic modes, the CTA
sensitivity will be well below the thermal value of the annihilation
cross-section. In this case, even with larger systematics, thermal dark matter
candidates up to masses of a few TeV will be easily studied.
