The film-forming capability and protective properties of alginate extracted from Sargassum and fucoidan extracted from Laminaria have led to their use as antimicrobial and antioxidant coatings in modern packaging methods to prevent the rapid spoilage of aquatic products. In this study, alginate and fucoidan were extracted from the brown algae Sargassum and Laminaria through a combined chemical process in the laboratory, and coatings were prepared from them. Subsequently, alginate films, fucoidan films, and composite alginate/fucoidan films were produced, and their properties were evaluated using microbial analyses, FTIR, SEM, and DSC characterization techniques. In the next stage, the effect of the prepared alginate and fucoidan films in four treatments on the shelf life and quality of whiteleg shrimp (Litopenaeus vannamei) including total bacterial count, psychrophilic bacteria count, thiobarbituric acid index, free fatty acids, TVBN, pH, TMA, and sensory evaluation was statistically compared with coated samples (treatments 1–3) and the control sample (polymer plastic coating) during 14 days of refrigerated storage. Based on the results obtained in this study, all measured variables showed significant differences between shrimp fillets coated with alginate (T1), fucoidan (T2), and the composite alginate/fucoidan film (T3) compared to the control sample (T4) and also among each other (P < 0.05). Furthermore, the use of the composite alginate–fucoidan film (T3) significantly increased the shelf life of white leg shrimp during refrigerated storage compared to the other treatments and the control.