2-Azidoazirines, sufficiently stable to be isolated in good yields, were synthesized by the cascade SN2'-SN2' substitution of bromine in methyl 2-bromo-2H-azirine-2-carboxylates using sodium azide in acetonitrile. According to the DFT calculations, the first step, Br/N3 exchange, is rate-determining and occurs in a concerted manner, while the subsequent N3/N3 exchange is a stepwise process. An alternative method using the TMSN3/Et3N/CH2Cl2 system permits the isolation in pure form of only 2-azidoazirines having ortho-substituted aryl substituent at C3, although it is more efficient in a one-pot synthesis of 1-(azirin-2-yl)-1,2,3-triazoles from the bromoazirines via the “cascade SN2'-SN2' substitution/CuAAC reaction” sequence. The protocol has a broad scope for both azirines and alkynes and provides good product yields. The described CuAAC reaction of 2-azidoazirines represents the first example of a copper(I)-catalyzed reaction of azirines that occurs with the preservation of the azirine ring.