The present invention provides several non-naturally occurring sulfotransferase enzymes that have been engineered to react with aryl sulfate compounds as sulfo group donors, instead of the natural substrate 3′-phosphoadenosine 5′-phosphosulfate (PAPS), and with heparosan-based polysaccharides, particularly heparan sulfate, as sulfo group acceptors. Each of the engineered sulfotransferase enzymes have a biological activity characterized by the position within the heparosan-based polysaccharide that receives the sulfo group, including glucosaminyl N-sulfotransferase activity, hexuronyl 2-O sulfotransferase activity, glucosaminyl 6-O sulfotransferase activity, or glucosaminyl 3-O sulfotransferase activity. Methods of using the engineered sulfotransferases to produce sulfated heparosan-based polysaccharides, including polysaccharides having anticoagulant activity, are also provided.