Catalyzes the reaction that attaches fucose through an O-glycosidic linkage to a conserved serine or threonine residue in the consensus sequence C1-X-X-S/T-C2 of thrombospondin type I repeats (TSRs) where C1 and C2 are the first and second cysteines of the repeat, respectively (PubMed:22588082). O-fucosylates members of several protein families including the ADAMTS, the thrombospondin (TSP) and spondin families (Probable) (PubMed:17395588). Required for the proper secretion of ADAMTS family members such as ADAMTSL1 and ADAMTS13 (PubMed:17395588, PubMed:17395589). The O-fucosylation of TSRs is also required for restricting epithelial to mesenchymal transition (EMT), maintaining the correct patterning of mesoderm and localization of the definite endoderm (By similarity).