Unrepaired or inaccurately repaired DNA damage can lead to a range of cell fates, such as apoptosis, cellular senescence or cancer, depending on the efficiency and accuracy of DNA damage repair and on the downstream DNA damage signalling. DNA damage repair and signalling have been studied and modelled in detail separately, but it is not yet clear how they integrate with one another to control cell fate. In this study, we have created an integrated stochastic model of DNA damage repair by non-homologous end joining and of gamma irradiation-induced cellular senescence in human cells that are not apoptosis-prone. The integrated model successfully explains the changes that occur in the dynamics of DNA damage repair after irradiation. Simulations of p53/p21 dynamics after irradiation agree well with previously published experimental studies, further validating the model. Additionally, the model predicts, and we offer some experimental support, that low-dose fractionated irradiation of cells leads to temporal patterns in p53/p21 that lead to significant cellular senescence. The integrated model is valuable for studying the processes of DNA damage induced cell fate and predicting the effectiveness of DNA damage related medical interventions at the cellular level.