Initialized climate model simulations have proven skillful for near-term predictability of the key physical climate variables. By comparison, predictions of biogeochemical fields like ocean carbon flux, are still emerging. Initial studies indicate skillful predictions are possible for lead-times up to six years at global scale for some CMIP6 models. However, unlike core physical variables, biogeochemical variables are not directly initialized in existing decadal preciction systems, and extensive empirical parametrization of ocean-biogeochemistry in Earth System Models introduces a significant source of uncertainty. Here, we propose a new approach for improving the skill of decadal ocean carbon flux predictions using observationally-constrained statistical models, as alternatives to the ocean-biogeochemistry models. We use observations to train multi-linear and neural-network models to predict the ocean carbon flux. To account for observational uncertainties, we train using six different observational estimates of the flux. We then apply these trained statistical models using input predictors from the Canadian Earth System Model (CanESM5) decadal prediction system to produce new decadal predictions. Our hybrid GCM-statistical approach significantly improves prediction skill, relative to the raw CanESM5 hindcast predictions over 1990-2019. Our hybrid-model skill is also larger than that obtained by any available CMIP6 model. Using bias-corrected CanESM5 predictors, we make forecasts for ocean carbon flux over 2020-2029. Both statistical models predict increases in the ocean carbon flux larger than the changes predicted from CanESM5 forecasts. Our work highlights the ability to improve decadal ocean carbon flux predictions by using observationally-trained statistical models together with robust input predictors from GCM-based decadal predictions.