The present work applies a model for microstructural evolution in the solid state and Al-Cu-Mg alloys and expands it in a computationally efficient way to include solid-liquid reactions in fusion welds. The model is used to predict local strength and hardness of the welds, using a formulation that incorporates hardening due to two types of precipitates, i.e. Cu-Mg co-clusters and the S phase precipitates. The model predictions are compared with hardness, differential scanning calorimetry and transmission electron microscopy data for a fusion welded 2024-T351 aluminium alloy. The model predicts solid state reactions and solid-liquid reactions including co-cluster dissolution, S phase formation, growth, coarsening and dissolution, co-cluster reformation on cooling, and solute partitioning on resolidification. The model predictions are in good agreement with the experimental results and illustrate the dominant role that (sub-)nanoscale co-clusters play in strengthening of welds. The yield strength of as welded material tested normal to the weld is mainly due to the co-clusters.