Fiducial cross-sections for $t\bar{t}$ production with one or two additional $b$-jets are presented, using an integrated luminosity of 20.3 fb${}^{-1}$ of proton-proton collisions at a centre-of-mass energy of 8 TeV at the Large Hadron Collider, collected with the ATLAS detector. The cross-section times branching ratio for $t\bar{t}$ events with at least one additional $b$-jet is measured to be 950 $\pm$ 70 (stat.) ${}^{+240}_{-190}$ (syst.) fb in the lepton-plus-jets channel and 50 $\pm$ 10 (stat.) ${}^{+15}_{-10}$ (syst.) fb in the $e\mu$ channel. The cross-section times branching ratio for events with at least two additional $b$-jets is measured to be 19.3 $\pm$ 3.5 (stat.) $\pm$ 5.7 (syst.) fb in the dilepton channel ($e\mu$, $\mu\mu$, $ee$) using a method based on tight selection criteria, and 13.5 $\pm$ 3.3 (stat.) $\pm$ 3.6 (syst.) fb using a looser selection that allows the background normalisation to be extracted from data. The latter method also measures a value of 1.30 $\pm$ 0.33 (stat.) $\pm$ 0.28 (syst.)$\%$ for the ratio of $t\bar{t}$ production with two additional $b$-jets to $t\bar{t}$ production with any two additional jets. NB: When merging several output YODA files, the ratio (d02-x01-y01) needs to be reconstructed in a post-processing step.