A comprehensive approach to the management of brown seaweed—Fucus vesiculosuswas presented. An algal extract, which served as a biostimulant of plant growth was produced using ultrasound-assisted extraction (UAE). The concentration of the extract (20, 40, 60, 80, 100%), which had the greatest influence on biometric parameters of radish, was determined in germination tests. The seaweed itself as well as the produced post-extraction residue were used in doses of 2 and 4 g/kg as soil additives, stimulating plant growth in the initial phase. Pot tests for sorghum carried out under optimal conditions (20% extract and 2 g/kg of soil additive) had a positive effect on the plant weight, length and the content of chlorophyll in comparison with the control group treated with distilled water. Additionally, preliminary studies on the bioremediation of soil contaminated with Zn(II) ions with the use of both soil additives were performed. It was shown that the immobilization of Zn(II) ions in the soil by the applied additives reduced the bioaccumulation of zinc in the aerial part of plants as compared with the group cultivated in the contaminated soil but without additive. Accordingly, by producing plant biostimulants by UAE it was also possible to successfully manage the post-extraction residue following the concept of a bio-based economy.