The aim of this study was to optimize the acidic treatment of the brown alga Ecklonia radiata in order to extract fucoidan and facilitate the efficient sequential extraction of alginates. Response surface methodology was used to determine the effects of the temperature, pH, and duration of the acidic treatment on fucoidan yield, alginate extractability, and the molecular weight of sequentially extracted alginates. Desirability functions were then used to predict the best overall combinations of responses. The most desirable compromise allowed for the recovery of a fucoidan-rich fraction with a yield of 3.75% (w/w of alga) and the sequential extraction of alginates having an average molecular weight of 730. kDa at a yield of 44% (w/w of alga), with low cross-contamination between the products. The optimized acidic treatment could form the basis of an industrial biorefinery process for the production of both fucoidan and alginate.