We present a self-consistent, absolute isochronal age scale for young (< 200 Myr), nearby (< 100 pc) moving groups in the solar neighbourhood based on homogeneous fitting of semi-empirical pre-main-sequence model isochrones using the tau^2 maximum-likelihood fitting statistic of Naylor & Jeffries in the M_V, V-J colour-magnitude diagram. The final adopted ages for the groups are: 149+51-19 Myr for the AB Dor moving group, 24+/-3 Myr for the {beta} Pic moving group (BPMG), 45+11-7 Myr for the Carina association, 42+6-4 Myr for the Columba association, 11+/-3 Myr for the {eta} Cha cluster, 45+/-4 Myr for the Tucana-Horologium moving group (Tuc-Hor), 10+/-3 Myr for the TW Hya association, and 22+4-3 Myr for the 32 Ori group. At this stage we are uncomfortable assigning a final, unambiguous age to the Argus association as our membership list for the association appears to suffer from a high level of contamination, and therefore it remains unclear whether these stars represent a single population of coeval stars. Our isochronal ages for both the BPMG and Tuc-Hor are consistent with recent lithium depletion boundary (LDB) ages, which unlike isochronal ages, are relatively insensitive to the choice of low-mass evolutionary models. This consistency between the isochronal and LDB ages instills confidence that our self-consistent, absolute age scale for young, nearby moving groups is robust, and hence we suggest that these ages be adopted for future studies of these groups. Software implementing the methods described in this study is available from http: //www.astro.ex.ac.uk/people/timn/tau-squared/.