This paper describes the concept, technical realisation and validation of a largely data-driven method to model events with Z→ττ decays. In Z→μμ events selected from proton-proton collision data recorded at √s=8 TeV with the ATLAS experiment at the LHC in 2012, the Z decay muons are replaced by τ leptons from simulated Zarrowττ decays at the level of reconstructed tracks and calorimeter cells. The τ lepton kinematics are derived from the kinematics of the original muons. Thus, only the well-understood decays of the Z boson and τ leptons as well as the detector response to the τ decay products are obtained from simulation. All other aspects of the event, such as the Z boson and jet kinematics as well as effects from multiple interactions, are given by the actual data. This so-called τ-embedding method is particularly relevant for Higgs boson searches and analyses in ττ final states, where Zarrowττ decays constitute a large irreducible background that cannot be obtained directly from data control samples. In this paper, the relevant concepts are discussed based on the implementation used in the ATLAS Standard Model H→ττ analysis of the full datataset recorded during 2011 and 2012.