An efficient base-catalyzed, metal-free method for the synthesis of 5-amino-1,2,3-triazole-4-N-sulfonyl- and arylimidamides, directed by the structure of the amidine group, has been developed. It is based on a previously unknown tandem process involving cycloaddition reaction to 3,3-diaminoacrylonitriles (2-cyanoacetamidines) with aryl(alkyl)sulfonyl or aryl azides and Cornforth-type rearrangement. During the reaction optimization, different factors were found to facilitate the title reaction, which include the use of a strong base and N-mono- or N,N'-disubstituted 3,3-diaminoacrylonitriles. The reaction is tolerant to variously N-monosubstituted and N,N'-disubstituted 3,3-diaminoacrylonitriles and to various aryl- and aryl/alkyl sulfonyl azides. The developed method has a broad scope and can be applied to obtain a variety of 5-amino-1,2,3-triazole-4-carbimidamides bearing at the N1 position alkyl, allyl, propargyl, benzyl, cycloalkyl, and heteroaryl substituents and sulfonyl and aryl substituents at the amidine group. Post-cyclization reactions of prepared 5-amino-1,2,3-triazoles with DMF-DMA DMA-DMF leads to 1,2,3-triazolo[4,5-d]pyrimidines, 8-aza purine analogues demonstrating the applicability of the prepared compounds in organic synthesis.