Using the almost all-sky 2MASS Photometric Redshift catalogue (2MPZ) we perform for the first time a tomographic analysis of galaxy angular clustering in the local Universe (z < 0.24). We estimate the angular auto- and cross-power spectra of 2MPZ galaxies in three photometric redshift bins, and use dedicated mock catalogues to assess their errors. We measure a subset of cosmological parameters, having fixed the others at their Planck values, namely the baryon fraction fb=0.14^{+0.09}_{-0.06}, the total matter density parameter Ωm = 0.30 ± 0.06, and the effective linear bias of 2MPZ galaxies beff, which grows from 1.1^{+0.3}_{-0.4} at = 0.05 up to 2.1^{+0.3}_{-0.5} at = 0.2, largely because of the flux-limited nature of the data set. The results obtained here for the local Universe agree with those derived with the same methodology at higher redshifts, and confirm the importance of the tomographic technique for next-generation photometric surveys such as Euclid or Large Synoptic Survey Telescope.