Different azides and alkynes have been coupled via Cu-catalyzed 1,3-dipolar Huisgen cycloaddition to afford a novel family of N1- and C5-substituted 1,2,3-triazole derivatives that feature the propargylamine group typical of irreversible MAO-B inhibitors at the C4-side chain of the triazole ring. All the synthesized compounds were evaluated against human MAO-A and MAO-B. Structure-activity relationships and molecular modeling were utilized to gain insight into the structural and chemical features that enhance the binding affinity and selectivity between the two enzyme isoforms. Several lead compounds, in terms of potency (submicromolar to low micromolar range), MAO-B selective recognition, and brain permeability, were identified. One of these leads (MAO-B IC50 of 3.54 μM, selectivity MAO-A/MAO-B index of 27.7) was further subjected to reversibility and time-dependence inhibition studies, which disclosed a slow and irreversible inhibition of human MAO-B. Overall, the results support the suitability of the 4-triazolylalkyl propargylamine scaffold for exploring the design of multipotent anti-Alzheimer compounds endowed with irreversible MAO-B inhibitory activity.