A copper-catalysed hydroamination reaction of N-allenylsulfonamides with amines has been developed through a rational approach based on mechanistic studies. The reaction is promoted by a simple copper(I) catalyst and proceeds at room temperature with complete regioselectivity and excellent stereoselectivity towards linear (E)-N-(3-aminoprop-1-enyl)sulfonamides. Density Functional Theory (DFT) studies allow interpreting the key role of unsaturated substituents on nitrogen as ancillary coordinating moieties for the copper catalyst.