Measurements of the jet activity in tt¯ events produced in proton-proton collisions at s=8 TeV are presented, using 20.3 fb−1 of data collected by the ATLAS experiment at the Large Hadron Collider. The events were selected in the dilepton eμ decay channel with two identified b-jets. The numbers of additional jets for various jet transverse momentum (pT) thresholds, and the normalised differential cross-sections as a function of pT for the five highest-pT additional jets, were measured in the jet pseudo-rapidity range |η| < 4.5. The gap fraction, the fraction of events which do not contain an additional jet in a central rapidity region, was measured for several rapidity intervals as a function of the minimum pT of a single jet or the scalar sum of pT of all additional jets. These fractions were also measured in different intervals of the invariant mass of the eμbb¯ system. All measurements were corrected for detector effects, and found to be mostly well-described by predictions from next-to-leading-order and leading-order tt¯ event generators with appropriate parameter choices. The results can be used to further optimise the parameters used in such generators.[Figure not available: see fulltext.]