This study investigated the effects of the replacement ratio of natural aggregates (NAs) by recycled aggregate (RAs), the replacement ratio of cement by rice husk ash (RHA), and their interaction on compressive properties of recycled aggregate concrete (RAC). The RAs used consisted of 37.5 wt% recycled brick aggregates and 62.5 wt% recycled concrete aggregates from construction and demolition waste. To optimise the properties of RAC mixture, a full factorial design of experiment was applied in designing the concrete mixture proportion. The two factors considered were: the replacement ratio (wt.%) of RA with five levels (0%, 30%, 50%, 70% and 100%) and the replacement ratio (wt.%) of RHA with four levels (0%, 10%, 20% and 30%). Axial compression tests based on the full factorial experiment were conducted on cubic and prismatic samples at 28 days to evaluate their compressive properties. In addition, further cubic concrete groups were also tested in axial compression at different concrete ages (i.e., 3, 7, 28, 56 and 91 days) to understand the effect of concrete age on the compressive strength. Statistical analyses including ANOVA, post-hoc pairwise comparisons and effect size (Cohen's d) computation were performed to evaluate the experimental results. The results indicated that the compressive strength of concrete at 28 days was significantly affected by the replacement ratio of RA and RHA (both p-values <0.0001), as well as their interaction (p-value = 0.0001). For the four different replacement ratios (0%, 10%, 20% and 30%) of RHA considered in this study, the optimised ratio was 10%, which resulted in 0.4% and 4.9% increases in compressive strength of NAC and RAC (RA replacement ratio = 100%), respectively. RHA contributed more to the strength improvement of RAC than to that of NAC, both at 28 days and at 91 days. A new compressive strength model was developed for concrete containing RAs and RHA (or for other supplementary cementitious materials such as fly ash, silica fume, metakaolin and ground granulated blast slag). The validation with the experimental results from the literature showed a good accuracy of this model for concrete strength prediction, with 4.45% mean absolute percentage error and 2.3 root mean square error.